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Linear Operators and Matrices pp 9–19Cite as

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List of Publications of Peter Lancaster

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Part of the book series: Operator Theory: Advances and Applications ((OT,volume 130))

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References

Monographs and Textbooks

  1. Lancaster, P., Lambda-matrices and Vibrating Systems, Pergamon Press, 1966.

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  2. Lancaster, P., Theory of Matrices, Academic Press, 1969, MR 39, 6885. MR 80a, 15001. MR 84b, 15004.

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  3. Lancaster, P., Mathematics: Models of the Real World, Prentice-Hall, 1976.

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  4. Gohberg, I., Lancaster, P. and Rodman, L., Matrix Polynomials, Academic Press, 1982. MR 84c, 15012.

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  5. Gohberg, I., Lancaster, P. and Rodman, L., Matrices and Indefinite Scalar Products, Birkhäuser Verlag, 1983. MR 87j, 15001.

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  6. Lancaster, P. and Tismenetsky, M., Theory of Matrices, 2nd edition, Academic Press, 1985. MR 87a, 15001.

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  7. Lancaster, P. and Salkauskas, K., Curve and Surface Fitting, Academic Press, 1986.

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  8. Gohberg, I., Lancaster, P. and Rodman, L., Invariant Subspaces of Matrices with Applications, John Wiley (Canadian Math. Soc. Monographs), 1986. MR 88a, 15001.

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  9. Lancaster, P. and Rodman, L., Solutions of the Continuous and Discrete Time Algebraic Riccati Equations: A Review, Chapter 2 of The Riccati Equation, (Ed. Bittanti, Laub and Willems) Springer Verlag, 1991. MR 92d, 93008.

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  10. Lancaster, P. and Rodman, L., Algebraic Riccati Equations, Oxford University Press, 1995.

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  11. Lancaster, P. and Salkauskas, K., Transform Methods in Applied Mathematics: An Introduction, John Wiley, New York, 1996.

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  12. Lancaster, P., Lecture Notes on Linear Algebra, Control, and Stability, Centro Internacional de Matemática, Coimbra, 1998. (59 pages) (2nd Edition, Dept. of Math. and Stat., University of Calgary, 1999. (72 pages)

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Research Papers

  1. Lancaster, P., Free vibration and hysteretic damping, J. Roy. Aero. Soc., 64 (1960), p. 229.

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  2. Lancaster, P., Free vibrations of lightly damped systems by perturbation methods, Quart. J. Mech. Appl. Math., 13 (1960), pp. 138–155. MR 22, 4153.

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  3. Lancaster, P., Inversion of Lambda-Matrices and application to the theory of linear vibrations, Arch. Rat. Mech. Anal., 6 (1960), pp. 105–114. MR 22, 8029.

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  4. Lancaster, P., Expressions for damping matrices in linear vibration problems, J. Aero. Sp. Sci., 28 (1961), p. 256.

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  5. Lancaster, P., Direct solution of the flutter problem, (British) MM. of Aviation R. and M., 3206 (1961).

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  6. Lancaster, P., A generalised Rayleigh Quotient Iteration for Lambda matrices, Arch. Rat. Mech. Anal., 8 (1961), pp. 209–322. MR 25, 2697.

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  7. Lancaster, P., Some applications of the Newton-Raphson method to nonlinear matrix problems, Proc. Roy. Soc. (London), Ser. A., 271 (1963). MR 27, 925.

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  8. Lancaster, P., On regular pencils of matrices arising in the theory of vibrations, Quart. J. Mech. App. Math., 16 (1963), pp. 253–257. MR 27, 162.

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  9. Lancaster, P., Convergence of the Newton-Raphson method for arbitrary polynomials, Mathematical Gazette, 48 (1964), pp. 291–295. MR 29, 5380.

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  10. Lancaster, P., Bounds for latent roots in damped vibration problems, SIAM Review, 6 (1964), pp. 121–126. MR 29, 6632.

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  11. Lancaster, P., On eigenvalues of matrices dependent on a parameter, Num. Math., 6 (1964), pp. 377–387. MR 30, 1606.

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  12. Lancaster, P., Algorithms for Lambda-Matrices, Num. Math., 6 (1964) pp. 388–394. MR 30, 1607.

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  13. Lancaster, P., Error analysis for the Newton-Raphson method, Num. Math., 9 (1966), pp. 55–68. MR 35, 1208.

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  14. Lancaster, P. and Webber, P.N., Jordan Chains for Lambda-matrices, Lin. Alg. & Appls., 1 (1968), pp. 563–569. MR 39, 228.

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  15. Pattabhiraman, M.V. and Lancaster, P., Spectral properties of a polynomial operator, Num. Math., 13 (1969), pp. 247–259. MR 40, 775.

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  16. Rokne, J. and Lancaster, P., Automatic errorbounds for the approximate solution of equations, Computing (1969), pp. 294–303. MR 41, 2966.

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  17. Lancaster, P. Spektraleigenschaften von Operatorfunktionen. Contribution to Iterationsverfahren, Numerische Mathematik, Approximation Theorie, Int. Schr. Num. Math., Vol. 15, pp. 53–60, Birkhäuser, Basel (1970). MR 51, 6467.

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  18. Lancaster, P., Explicit solutions of linear matrix equations, SIAM Rev., 12 (1970), pp. 544–566.

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  19. Lancaster, P., Jordan chains for Lambda-matrices II, Aequationes Mathematicae, 5 (1970), pp. 290–293. MR 52, 2312

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  20. Lancaster, P. Some questions in the classical theory of vibrating systems, Bull. Poly. Inst. Jassy, 17 (1971), pp. 125–132. MR 52, 2312.

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  21. Rokne, J. and Lancaster, P., Complex interval arithmetic, Comm Assoc. Comp. Mach., 14 (1971), pp. 111–112.

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  22. Lancaster, P. and Farahat, H.K., Norms on direct sums and tensor products, Math. of Comp., 26 (1972), pp. 401–414. MR 46, 4229.

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  23. Lancaster, P., A note on sub-multiplicative norms, Num. Math., 19 (1972), pp. 206–208. MR 46, 4230.

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  24. Schmidt, E. and Lancaster, P., L-splines for constant coefficient differential operators, Proc. Manitoba Conf. on Num. Math., U. of Manitoba (1971). MR 49, 7656.

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  25. Cross, G.W. and Lancaster, P., Square roots of complex matrices, J. Lin. Mult. Alg., 1 (1974), pp. 288–293. MR 49, 5033.

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  26. Schmidt, E., Lancaster, P., and Watkins, D., Bases of spline functions associated with constant coefficient differential operators, SIAM J. Num. Anal., 12 (1975), pp. 630–645. MR 52, 8728.

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  27. Rokne, J. and Lancaster, P., Complex interval arithmetic: algorithms, Comp. J., 18 (1975), pp. 83–85.

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  28. Lancaster, P. and Wimmer, H.K., Zur theorie der λ-matrizen, Math. Nach., 68 (1975), pp. 325–330. MR 58, 28036.

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  29. Lancaster, P. and Terray, J., Numerical solution of a boundary value problem arising in the study of heat transfer. Contribution to Numerische Losung von Differentialgleichungen, Int. Schr. Num. Math., Vol. 27 pp. 303–308, Birkhauser, Basel, 1975. MR 53, 4757.

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  30. Lancaster, P., An efficient computation of the angle of latitude, J. Can. Soc. Expl. Geophysicists, 11 (1975), pp. 72–73.

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  31. Lancaster, P., Interpolation in a rectangle and finite elements of high degree, J. Inst. Math. Appl., 18 (1976), pp. 65–77. MR 56, 13614.

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  32. Lancaster, P., and Watkins, D., Interpolation in the plane and rectangular finite elements. Contribution to Numerische Behandlung von Differentialgleichungen, insbesondere mit der Methode der finiten Elemente, Int. Schr. Num. Math., Vol. 31, pp. 125–145, Birkhauser, Basel, 1976. MR 58, 24849.

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  33. Terray, J. and Lancaster, P., On the numerical calculation of eigenvalues and eigenvectors of operator polynomials, J. Math. Anal. Appl., 60 (1977), pp. 370–378. MR 58, 24928.

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  34. Lancaster, P. and Rokne, J.G., Solutions of nonlinear operator equations, SIAM J. Math. Anal., 8 (1977), pp. 448–457. MR 55, 11078.

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  35. Watkins, D. and Lancaster, P., Some families of finite elements, J. Inst. Math. Appl., 19 (1977), pp. 385–397. MR 55, 11650.

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  36. Lancaster, P. A fundamental theorem on Lambda-matrices with applications I: ordinary differential equations with constant coefficients, Lin. Alg. & Appl., 18 (1977), pp. 189–211. MR 58, 5711.

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  37. Lancaster, P., A fundamental theorem on Lambda-matrices with applications II: difference equations with constant coefficients, Lin. Alg. & Appl., 18 (1977), pp. 213–222. MR 58, 5712.

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  38. Gohberg, I., Lancaster, P., and Rodman, L., Spectral analysis of matrix polynomials I: canonical forms and divisors, Lin. Alg. & Appl., 20 (1978), pp. 144. MR 57, 3155.

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  39. Gohberg, I., Lancaster, P., and Rodman, L., Spectral analysis of matrix polynomials II: the resolvent form and spectral divisors, Lin. Alg. & Appl., 21 (1978), pp. 65–88. MR 58, 16720.

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  40. Gohberg, I., Lancaster, P., and Rodman, L., Representations and divisibility of operator polynomials, Can. J. Math., 30 (1978), pp. 1045–1069. MR 80a, 47024.

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  41. Lancaster, P., Composite methods for generating surfaces. Contribution to Polynomial and Spline Approximation, ed. B.N. Sahney, Reidel Pub. Co. (1979), pp. 91–102. MR 81c, 41075.

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  42. Lancaster, P., Moving weighted least squares methods. Contribution to Polynomial and Spline Approximation, ed. B.N. Sahney, Reidel Pub. Co. (1979), pp. 103–120. MR 80c, 6503.

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  43. Gohberg, I., Lancaster, P. and Rodman, L., Perturbation theory for divisors of operator polynomials, SIAM J. Math. Anal., 10 (1979), pp. 1161–1183. MR 82b, 4701b.

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  44. Gohberg, I., Lancaster, P. and Rodman, L., On selfadjoint matrix polynomials, Integral Eq. and Op. Theory, 2 (1979), pp. 434–439. MR 80k, 15018.

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  45. Lancaster, P. and Rodman, L., Existence and uniqueness theorems for the algebraic Riccati equation, Int. J. Control, 32 (1980), pp. 285–309. MR 82c, 15017.

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  46. Barnett, S. and Lancaster, P., Some properties of the Bezoutian for polynomial matrices, J. Lin. Mult. Alg., 9 (1980), 99–110. MR 82c, 15014.

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  47. Gohberg, I., Lancaster, P. and Rodman, L., Spectral analysis of selfadjoint matrix polynomials, Annals of Math., 112 (1980), pp., 33–71. MR 82c, 15010.

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  48. Barnett, S. and Lancaster, P., Matrices having striped inverse. Progress in Cybernetics and Systems Research, Vol. 8, pp. 333–336. Edited by R. Trappl, G.J. Klir and F. Pichler, Hemisphere Publishing Corporation, Washington, D.C., 1981.

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  49. Lancaster, P. and Salkauskas, K., Surfaces generated by moving least squares methods, Math. Soc. Comp., 37 (1981), pp. 141–158. MR 83c, 65015.

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  50. Gohberg, I., Lancaster, P. and Rodman, L., Factorization of self-adjoint matrix polynomials with constant signature, J. Lin. Mult. Alg., 11 (1982), pp. 209–224. MR 83c, 15011.

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  51. Gohberg, I., Lancaster, P. and Rodman, L., Perturbations of H self-adjoint matrices with applications to differential equations, Integral Eq. and Op. Theory, 5 (1982), pp. 718–757.

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  52. Lancaster, P. and Pattabhiraman, M.V., The local determination of Jordan bases for H-selfadjoint operators, Lin. Alg. and Appl., 48 (1982), pp. 191–199. MR 84a, 15009.

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  53. Lancaster, P. and Rozsa, P., On the matrix equation AX + X* A* = C, SIAM J. Alg. and Discrete Methods, 4 (1983), pp. 432–436.

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  54. Lancaster, P. and Tismenetsky, M., Inertia characteristics of self-adjoint matrix polynomials, Lin. Alg. and Appl., 52 (1983), pp. 479–496.

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  55. Lancaster, P. and Tismenetsky, M., Some extensions and modifications of classical stability tests for polynomials, Inter. J. Control, 38 (1983), pp. 369–380.

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  56. Gohberg, I., Lancaster, P. and Rodman, L., A sign-characteristic for selfadjoint meromorphic matrix functions, Applicable Analysis, 16 (1983), pp. 165–185.

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  57. Gohberg, I., Lancaster, P. and Rodman, L., A sign characteristic for rational matrix functions, Mathematical Theory of Networks and Systems, pp. 363–369. Edited by P.A. Fuhrmann. Springer Verlag, Berlin, 1984.

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  58. Lancaster, P., Lerer, L. and Tismenetsky, M., Factored forms for solutions of AX - X B = C and X - AX B = C in companion matrices, Lin. Alg. and Appl., 62 (1984), pp. 19–49.

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  59. Lancaster, P. and Rozsa, P., Eigenvectors of H-selfadjoint matrices, Zeitschrift far Ang. Math. and Mech., 64 (1984), pp. 439–441.

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  60. Lancaster, P. and Maroulas, J., The kernel of the bezoutian for operator polynomials, J. Lin. Mult. Alg., 17 (1985), pp. 181–201.

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  61. Gohberg, I., Lancaster, P. and Rodman, L., Perturbations of analytic hermitian matrix functions, Applicable Analysis, 20 (1985), pp. 23–48. MR 87d, 15018.

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  62. Elsner, L. and Lancaster, P., The spectral variation of pencils of matrices, Jour. Computational Math., 3 (1985), pp. 262–274. MR 87j, 15029.

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  63. Koltracht, I. and Lancaster, P., Condition numbers of Toeplitz and blockToeplitz matrices, Operator Theory: Advances and Applications, Vol. 18 (1986), pp. 271–300. MR 88i, 15015.

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  64. Gohberg, I., Lancaster, P. and Rodman, L., On hermitian solutions of the symmetric algebraic Riccati equation, SIAM J. of Control and Optim., Vol. 24 (1986), pp. 1323–1334. MR 88f, 93041.

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  65. Gohberg, I., Lancaster, P. and Rodman, L., Quadratic matrix polynomials with a parameter, Advances in Applied Math., 7 (1986), pp. 253–281. MR 88e, 47027.

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  66. Lancaster, P., Ran, A.C.M. and Rodman, L., Hermitian solutions of the discrete algebraic Riccati equation, Int. J. Control., 44 (1986), pp. 777–802. MR 87h, 93022.

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  67. Lancaster, P. Common eigenvalues, divisors, and multiples of matrix polynomials: a review, Lin. Alg. and Appl., 84 (1986), pp. 139–160. MR 87m, 15032.

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  68. Lancaster, P. and Maroulas, J., Inverse eigenvalue problems for damped vibrating systems, J. Math. Anal. Appl., 123 (1987), pp. 238–261. MR 88d, 34013.

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  69. Lancaster, P., Ran, A.C.M. and Rodman, L., An existence and monotonicity theorem for the discrete algebraic matrix Riccati equation, J. Lin. Mult. Alg., 20 (1987), pp. 353–361. MR 88j, 93033.

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  70. Gohberg, I., Kailath, T., Koltracht, I. and Lancaster, P., Linear complexity parallel algorithms for linear systems of equations with recursive structure, Lin. Alg. and Appl., 88 (1987), pp. 271–315. MR 88g, 65027.

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  71. Gohberg, I., Koltracht, I. and Lancaster, P., Second order parallel algorithms for Fredholm integral equations with continuous displacement kernels, Integral Eq. and Op. Theory, 10 (1987), pp. 577–594. MR 88m, 65205.

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  72. Koltracht, I. and Lancaster, P., A definiteness test for Hankel matrices and their lower sub-matrices, Computing, 39 (1987), pp. 19–26. MR 88h, 15046.

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  73. Lancaster, P. and Maroulas J., Selective perturbation of spectral properties of vibrating systems using feedback, Lin. Alg. and Appl., 98 (1988), pp. 309–330. MR 88k, 93060.

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  74. Koltracht, I. and Lancaster, P., Generalized Schur parameters and the effects of perturbations, Lin. Alg. and Appl., 105 (1988), 109–129.

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  75. Koltracht, I. and Lancaster, P., Threshold algorithms for the prediction of reflection coefficients in a layered medium, Geophysics, 53 (1988), 908–919.

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  76. Lancaster, P. and Ye, Q., Inverse spectral problems for linear and quadratic matrix pencils, Lin. Alg. and Appl., 107 (1988), 293–309.

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  77. Gohberg, I., Kaashoek, M.A. and Lancaster, P., General Theory of regular matrix polynomials and band Toeplitz operators, Integral Eq. and Op. Theory, 11 (1988), 776–882.

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  78. Farid, F.O. and Lancaster, P., Spectral properties of diagonally dominant infinite matrices, Part I, Proc. Roy. Soc. Edinburgh, 111A (1989), 301–314.

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  79. Gohberg, I. Koltracht, I. and Lancaster, P., On the numerical solution of integral equations with piecewise continuous displacement kernels, Integral Eq. and Op. Theory, 12 (1989), 511–537.

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  80. Lancaster, P. and Ye, Q., Variational properties and Rayleigh quotient algorithms for symmetric matrix pencils, in the Gohberg Anniversary Collection, (Operator Theory and its Applications, Vol. 40, Birkhauser Verlag, Basel), (1989), 247–278. MR 91e, 65055.

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  81. Koltracht, I., Lancaster, P. and Smith, D., The structure of some matrices arising in tomography, Lin. Alg. and Appl., 130 (1990), 193–218. MR 91j, 65068.

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  82. Koltracht, I. and Lancaster, P., Constraining strategies for linear iterative processes, I.M.A. Jour. on Numerical Analysis, 10 (1990), 555–567. MR 91i, 65066.

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  83. Bruckstein, A., Kailath, T., Koltracht, I. and Lancaster, P., On the reconstruction of layered media from reflection data, SIAM J. Matrix Anal. and Appl., 12 (1991), 24–40. MR 92d, 86004.

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  84. Farid, F.O. and Lancaster, P., Spectral properties of diagonally dominant infinite matrices, Part II, Lin. Alg. and Appl. 143 (1991), 7–17. MR 91j, 47029.

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  85. Lancaster, P. and Ye, Q., Variational and numerical methods for symmetric matrix pencils, Bull. Australian Math. Soc., 43 (1991), 1–17. MR 91m, 65106.

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  86. Elsner, L., Koltracht, I. and Lancaster, P., Convergence properties of ART and SOR algorithms, Numer. Math., 59 (1991), pp. 91–106. MR 92i, 65065.

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  87. Jameson, A., Kreindler, E. and Lancaster, P., Symmetric, positive semidefinite, and definite real solutions of AX = X A T and AX = YB, Lin. Alg. and Appl., 160 (1992), 189–215. MR 92j, 15011.

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  88. Barkwell, L. and Lancaster, P., Overdamped and gyroscopic vibrating systems, Jour. of Appl. Mechanics, 59 (1992), 176–181. AMR 45 (5), #47.

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  89. Barkwell, L., Lancaster, P., and Markus, A.S., Gyroscopically stabilized systems: a class of quadratic eigenvalue problems with real spectrum, Canadian Jour. Math., 44 (1992), 42–53.

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  90. Gohberg, I., Koltracht, I. and Lancaster, P., Second order parallel algorithms for piecewise smooth displacement kernels, Integral Eq. and Op. Theory, 15 (1992), 16–29. MR 92h, 65199.

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  91. Lancaster, P., and Ye, Q., Definitizable hermitian matrix pencils, Aequationes Mathematicae, 46 (1993), 44–55.

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  92. Bohl, E. and Lancaster, P., Perturbation of spectral inverses applied to a boundary layer phenomenon arising in chemical networks, Lin. Alg. and Appl., 180 (1993), 35–59.

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  93. Andrew, A.L., Chu, K.W.E., and Lancaster, P., Derivatives of eigenvalues and eigenvectors of matrix functions, SIAM J. Matrix Anal. and Appl., 14 (1993), 903–926.

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  94. Lancaster, P., and Ye, Q., Rayleigh-Ritz and Lanczos methods for symmetric matrix pencils, Lin. Alg. and Appl., 185 (1993), 173–201.

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  95. Lancaster, P., Shkalikov, A., and Ye, Q., Strongly definitizable linear pencils in Hilbert space, Integral Eq. and Op. Theory, 17 (1993), 338–360.

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  96. Lancaster, P., Markus, A.S. and Ye, Q., Low rank perturbations of strongly definitizable transformations and matrix polynomials, Lin. Alg. and Appl., 197/198 (1994), 3–30.

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  97. Lancaster, P. and Shkalikov, A., Damped vibrations of beams and related spectral problems, Canadian Applied Math. Quarterly, 2 (1994), 45–90.

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  98. Lancaster, P. and Rodman, L., Invariant neutral subspaces for symmetric and skew real matrix pairs, Canadian Jour. of Math., 46 (1994), 602–618.

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  99. Lancaster, P., Markus, A.S., and Matsaev, V.I., Definitizable operators and quasihyperbolic operator polynomials, Jour. of Functional Analysis, 131 (1995), 1–28.

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  100. Lancaster, P. and Rodman, L., Minimal symmetric factorizations of symmetric real and complex rational matrix functions, Lin. Alg. and Appl. 220 (1995), 249–282.

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  101. Andrew, A.L., Chu, K.-w.E., and Lancaster, P., On numerical solution of nonlinear eigenvalue problems, Computing, 55 (1995), 91–111.

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  102. Krupnik, I., Lancaster, P. and Markus, A., Factorization of selfadjoint quadratic matrix polynomials with real spectrum, J. Lin. Mult. Alg., 39 (1995), 263–272.

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  103. Lancaster, P. and Rozsa, P., The spectrum and stability of a vibrating rail supported by sleepers, Computers and Mathematics with Applications, 31 (1996), 201–213.

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  104. Dai, H. and Lancaster, P., Linear matrix equations from an inverse problem of vibration theory, Lin. Alg. and Appl., 246 (1996), 31–47.

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  105. Krupnik, I., Lancaster, P. and Zizler, P., Factorization of selfadjoint matrix polynomials with real spectrum, J. Lin. Mult. Alg., 40 (1996), 327–336.

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  106. Lancaster, P., Markus, A.S. and Matsaev, V.I., Perturbations of G-selfadjoint operators and operator polynomials with real spectrum, in “Recent Developments in Operator Theory and its Applications”, Proceedings of the Winnipeg Conference, OT 87, Birkhäuser Verlag, Basel (1996), 207–221.

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  107. Lancaster, P., Markus, A.S. and Matsaev, V.I., Definitizable G-unitary operators and their applications to operator polynomials, in “Recent Developments in Operator Theory and its Applications”, Proceedings of the Winnipeg Conference, OT 87, Birkhäuser Verlag, Basel (1996), 222–232.

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  108. Lancaster, P., Markus, A.S. and Matsaev, V.I., Factorization of selfadjoint operator polynomials, Jour. of Operator Theory, 35 (1996), 337–348.

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  109. Lancaster, P., Markus, A.S. and Zizler, P., The order of neutrality for linear operators on indefinite inner product spaces, Lin. Alg. and Appl., 259 (1997), 25–29.

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  110. Dai, H. and Lancaster, P., Numerical methods for finding multiple eigenvalues of matrices depending on parameters, Numerische Math., 76 (1997), 189–208.

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  111. Dai, H. and Lancaster P., Newton’s method for a generalized inverse eigenvalue problem, Numerical Linear Algebra with Applications, 4 (1997), 1–21.

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  112. Krupnik, I. and Lancaster, P., H -selfadjoint and H -unitary matrix pencils, SIAM J. Matrix Anal. and Appl., 19 (1998), 307–324.

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  113. Krupnik, I. and Lancaster, P., Minimal pencil realizations of rational matrix functions with symmetries, Canadian Math. Bull. 41 (1998), 178–186.

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  114. Krupnik, I. and Lancaster, P., Linearizations, realization, and scalar products for regular matrix polynomials, Linear Algebra and its Applications, 272 (1998), 45–57.

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  115. Guo, Chun-Hua and Lancaster, P., Analysis and modification of Newton’s method for algebraic Riccati equations, Math. Comp., 67 (1998), 1089–1105.

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  116. Lancaster, P., Maroulas, J. and Zizler, P., The numerical range of self-adjoint matrix polynomials, Operator Theory: Advances and Applications, 106 (1998), 291–304.

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  117. Lancaster, P. and Kliem, W., Comments on stability properties of conservative gyroscopic systems, Jour. of Appl. Mech., 66 (1999), 272–273.

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  118. Lancaster, P. and Zizler, P., On the stability of gyroscopic systems, Jour. of Appl. Mech. 65 (1998), 519–522.

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  119. Guo, Chun-Hua and Lancaster, P., Iterative solution of two matrix equations, Math. Comp., 68 (1999), 1589–1603.

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  120. Freitas, P. and Lancaster, P., On the optimal spectral abscissa for a system of linear oscillators, SIAM J. Matrix Anal. and Appl. 21 (1999), 195–208.

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  121. Hryniv, R.O. and Lancaster, P., On the perturbation of analytic matrix functions, Integral Eq. and Op. Theory, 34 (1999), 325–338.

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  122. Lancaster, P., Strongly stable gyroscopic systems, Elec. Jour. of Linear Algebra, 5 (1999), pp. 53–66.

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  123. Hryniv, R.O., Lancaster, P. and Renshaw, A.A., A stability criterion for parameter dependent gyroscopic systems, Jour. of Appl. Mech., 66 (1999), 660–664.

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  124. Hryniv, R.O., Lancaster, P., Kliem, W. and Pommer, C., A precise bound for gyroscopic stabilization, Zeit. fiir Ang. Math. u. Mech., 80 (2000), 507–516.

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  125. Lancaster, P. and Markus, A. S., A note on factorization of analytic matrix functions, Operator Theory: Advances and Applications, 122 (2001), 323–330.

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  126. Hryniv, R. and Lancaster, P., Stabilization of gyroscopic systems, Zeit. fiir Ang. Math. u. Mech., (to appear).

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  127. Lancaster, P. and Psarrakos, P., The numerical range of selfadjoint quadratic matrix poynomials, SIAM J. Matrix Anal. and Appl., (to appear).

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  128. Lancaster, P. and Psarrakos, P., Normal and seminormal eigenvalues of matrix functions, Integral Eq. and Op. Theory, (to appear).

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Expositions, Surveys, etc.

  1. Lancaster, P., Some problems in aero-elasticity, Bull. Malayan Math. Soc., 5, (1958), pp. 27–33.

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  2. Lancaster, P., Some reflections on the “Easter Conference on Mathematics”, Bull. Malayan Math. Soc., 6 (1959), pp. 69–72.

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  3. Lancaster, P., The damped harmonic oscillator, Bull. Malayan Math. Soc., 6 (1959), pp. 96–99.

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  4. Lancaster, P., Approaching the speed of sound, NABLA: Bull. Malayan Math. Soc., 7 (1960), pp. 52–60.

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  5. Lancaster, P., A garden swing, NABLA: Bull. Malayan Math. Soc., 7 (1960), pp. 65–67.

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  6. Lancaster, P., Ill-conditioned equations, NABLA: Bull. Malayan Math. Soc., 7 (1960), pp. 165–167.

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  7. Lancaster, P., Symmetric transformations of the companion matrix, NABLA: Bull. Malayan Math. Soc., 8 (1961), pp. 146–148.

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  8. Lancaster, P., On Cooke’s extension of Simpson’s rule, NABLA: Bull. Malayan Math. Soc., 8 (1961), pp. 182–184.

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  9. Lancaster, P., Some numerical methods for solving equations: 1 and 2, NABLA: Bull. Malayan Math. Soc., 9 (1962), pp. 45–53 and 85–95.

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  10. Lancaster, P., A Centennial Expedition, Can. Alp. Jour., 51 (1968), pp. 209–211.

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  11. Lancaster, P., Applied mathematics in the undergraduate curriculum, Notes of the Can. Math. Congress, Vol. 5, No. 2 (1972), pp. 6–8.

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  12. Lancaster, P., A review of numerical methods for eigenvalue problems nonlinear in the parameter, Contribution to Numerik and Anwendungen von Eigenwertaufgaben and Verzweigungsproblemen, Int. Schr. Num. Math., 38 (1977), pp. 43–67. MR 58,19116.

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  13. Lancaster, P., Solving quadratic equations, Menemui Matematik, 1 (1979), 23–26. MR 81g 65001.

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  14. Lancaster, P., The transition from high school to university mathematics, Notes of the Can. Math. Soc., 12 (1980), pp. 8–21.

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  15. Lancaster, P., A review of recent results on factorization of matrix and operator-valued functions, Nonlinear Anal. and Applic., pp. 117–139. Edited by S.P. Singh and J.H. Burry, Marcel Dekker, New York, 1982. MR 84c, 15015.

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  16. Lancaster, P., Generalized Hermitian matrices: a new frontier for numerical analysis?, Proc. 9th Dundee Biennial Conf. on Num. Anal., pp. 179–189, Springer Verlag, Lecture Notes in Math., Vol. 912, 1982.

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  17. Lancaster, P., Mathematics and Society, The Canadian Encyclopedia, pp. 1099–1100, Hurtig Publishers, Edmonton, 1986. 2nd Edition, 1988.

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  18. Lancaster, P., Obituary: A.M. Ostrowski, Aequationes Mathematicae, 33 (1987), pp. 121–122. MR 88i, 01113.

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  19. Lancaster, P., What are universities for?, Position paper for the conference of the same title, University of Calgary, 1988.

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  20. Lancaster, P., Quadratic eigenvalue problems, Linear Alg. and Appl., 150 (1991), 499–506.

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  21. Andrew, A.L., Chu, K.W.E., and Lancaster, P., Sensitivities of eigenvalues and eigenvectors of problems nonlinear in the eigenparameter, Applied Mathematics Letters, 5(3), (1992), 69–72.

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  22. Lancaster, P., Spectra and stability of quadratic eigenvalue problems, Proceedings of the International Workshop on the Recent Advances in Applied Mathematics, Kuwait University, 1996.

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  23. Lancaster, P., The role of the Hamiltonian in the solution of algebraic Riccati equations, In “Dynamical Systems, Control, Coding, Computer Vision”, Eds. Picci, G., and Gillian, D. S., Birkhäuser, Basel, 1999, 157–172.

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Authors and Affiliations

  1. School of Mathematical Sciences Raymond and Beverly Sackler, Faculty of Exact Sciences Tel Aviv University, Ramat Aviv, 69978, Israel

    Prof. I. Gohberg

  2. Mathematik, Technische Universität Wien, Wiedner Hauptstrasse 8–10/1411, Wien, 1040, Austria

    Prof. H. Langer

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  1. Prof. I. Gohberg
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  1. School of Mathematical Sciences Raymond and Beverly Sackler, Faculty of Exact Sciences Tel Aviv University, Ramat Aviv, 69978, Israel

    I. Gohberg

  2. Mathematik, Technische Universität Wien, Wiedner Hauptstrasse 8–10/1411, Wien, 1040, Austria

    H. Langer

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Gohberg, I., Langer, H. (2002). List of Publications of Peter Lancaster. In: Gohberg, I., Langer, H. (eds) Linear Operators and Matrices. Operator Theory: Advances and Applications, vol 130. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-8181-4_2

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  • DOI: https://doi.org/10.1007/978-3-0348-8181-4_2

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