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List of Publications of Peter Lancaster

  • I. Gohberg
  • H. Langer
Conference paper
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Part of the Operator Theory: Advances and Applications book series (OT, volume 130)

Keywords

Matrix Polynomial Algebraic Riccati Equation Matrix Pencil Operator Polynomial Jordan Chain 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

Monographs and Textbooks

  1. B1.
    Lancaster, P., Lambda-matrices and Vibrating Systems, Pergamon Press, 1966.zbMATHGoogle Scholar
  2. B2.
    Lancaster, P., Theory of Matrices, Academic Press, 1969, MR 39, 6885. MR 80a, 15001. MR 84b, 15004.zbMATHGoogle Scholar
  3. B3.
    Lancaster, P., Mathematics: Models of the Real World, Prentice-Hall, 1976.zbMATHGoogle Scholar
  4. B4.
    Gohberg, I., Lancaster, P. and Rodman, L., Matrix Polynomials, Academic Press, 1982. MR 84c, 15012.zbMATHGoogle Scholar
  5. B5.
    Gohberg, I., Lancaster, P. and Rodman, L., Matrices and Indefinite Scalar Products, Birkhäuser Verlag, 1983. MR 87j, 15001.zbMATHGoogle Scholar
  6. B6.
    Lancaster, P. and Tismenetsky, M., Theory of Matrices, 2nd edition, Academic Press, 1985. MR 87a, 15001.zbMATHGoogle Scholar
  7. B6.
    Lancaster, P. and Salkauskas, K., Curve and Surface Fitting, Academic Press, 1986.zbMATHGoogle Scholar
  8. B7.
    Gohberg, I., Lancaster, P. and Rodman, L., Invariant Subspaces of Matrices with Applications, John Wiley (Canadian Math. Soc. Monographs), 1986. MR 88a, 15001.zbMATHGoogle Scholar
  9. B8.
    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.Google Scholar
  10. B9.
    Lancaster, P. and Rodman, L., Algebraic Riccati Equations, Oxford University Press, 1995.zbMATHGoogle Scholar
  11. B10.
    Lancaster, P. and Salkauskas, K., Transform Methods in Applied Mathematics: An Introduction, John Wiley, New York, 1996.zbMATHGoogle Scholar
  12. B11.
    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)Google Scholar

Research Papers

  1. 1.
    Lancaster, P., Free vibration and hysteretic damping, J. Roy. Aero. Soc., 64 (1960), p. 229.Google Scholar
  2. 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.MathSciNetzbMATHCrossRefGoogle Scholar
  3. 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.MathSciNetzbMATHCrossRefGoogle Scholar
  4. 4.
    Lancaster, P., Expressions for damping matrices in linear vibration problems, J. Aero. Sp. Sci., 28 (1961), p. 256.Google Scholar
  5. 5.
    Lancaster, P., Direct solution of the flutter problem, (British) MM. of Aviation R. and M., 3206 (1961).Google Scholar
  6. 6.
    Lancaster, P., A generalised Rayleigh Quotient Iteration for Lambda matrices, Arch. Rat. Mech. Anal., 8 (1961), pp. 209–322. MR 25, 2697.MathSciNetCrossRefGoogle Scholar
  7. 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.MathSciNetGoogle Scholar
  8. 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.MathSciNetzbMATHCrossRefGoogle Scholar
  9. 9.
    Lancaster, P., Convergence of the Newton-Raphson method for arbitrary polynomials, Mathematical Gazette, 48 (1964), pp. 291–295. MR 29, 5380.MathSciNetzbMATHCrossRefGoogle Scholar
  10. 10.
    Lancaster, P., Bounds for latent roots in damped vibration problems, SIAM Review, 6 (1964), pp. 121–126. MR 29, 6632.MathSciNetzbMATHCrossRefGoogle Scholar
  11. 11.
    Lancaster, P., On eigenvalues of matrices dependent on a parameter, Num. Math., 6 (1964), pp. 377–387. MR 30, 1606.MathSciNetzbMATHCrossRefGoogle Scholar
  12. 12.
    Lancaster, P., Algorithms for Lambda-Matrices, Num. Math., 6 (1964) pp. 388–394. MR 30, 1607.MathSciNetzbMATHCrossRefGoogle Scholar
  13. 13.
    Lancaster, P., Error analysis for the Newton-Raphson method, Num. Math., 9 (1966), pp. 55–68. MR 35, 1208.MathSciNetzbMATHCrossRefGoogle Scholar
  14. 14.
    Lancaster, P. and Webber, P.N., Jordan Chains for Lambda-matrices, Lin. Alg. & Appls., 1 (1968), pp. 563–569. MR 39, 228.MathSciNetzbMATHCrossRefGoogle Scholar
  15. 15.
    Pattabhiraman, M.V. and Lancaster, P., Spectral properties of a polynomial operator, Num. Math., 13 (1969), pp. 247–259. MR 40, 775.MathSciNetzbMATHCrossRefGoogle Scholar
  16. 16.
    Rokne, J. and Lancaster, P., Automatic errorbounds for the approximate solution of equations, Computing (1969), pp. 294–303. MR 41, 2966.Google Scholar
  17. 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.MathSciNetGoogle Scholar
  18. 18.
    Lancaster, P., Explicit solutions of linear matrix equations, SIAM Rev., 12 (1970), pp. 544–566.MathSciNetzbMATHCrossRefGoogle Scholar
  19. 19.
    Lancaster, P., Jordan chains for Lambda-matrices II, Aequationes Mathematicae, 5 (1970), pp. 290–293. MR 52, 2312MathSciNetzbMATHCrossRefGoogle Scholar
  20. 20.
    Lancaster, P. Some questions in the classical theory of vibrating systems, Bull. Poly. Inst. Jassy, 17 (1971), pp. 125–132. MR 52, 2312.MathSciNetGoogle Scholar
  21. 21.
    Rokne, J. and Lancaster, P., Complex interval arithmetic, Comm Assoc. Comp. Mach., 14 (1971), pp. 111–112.zbMATHGoogle Scholar
  22. 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.MathSciNetzbMATHCrossRefGoogle Scholar
  23. 23.
    Lancaster, P., A note on sub-multiplicative norms, Num. Math., 19 (1972), pp. 206–208. MR 46, 4230.MathSciNetzbMATHCrossRefGoogle Scholar
  24. 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.Google Scholar
  25. 25.
    Cross, G.W. and Lancaster, P., Square roots of complex matrices, J. Lin. Mult. Alg., 1 (1974), pp. 288–293. MR 49, 5033.MathSciNetGoogle Scholar
  26. 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.MathSciNetCrossRefGoogle Scholar
  27. 27.
    Rokne, J. and Lancaster, P., Complex interval arithmetic: algorithms, Comp. J., 18 (1975), pp. 83–85.zbMATHGoogle Scholar
  28. 28.
    Lancaster, P. and Wimmer, H.K., Zur theorie der λ-matrizen, Math. Nach., 68 (1975), pp. 325–330. MR 58, 28036.MathSciNetzbMATHCrossRefGoogle Scholar
  29. 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.MathSciNetGoogle Scholar
  30. 30.
    Lancaster, P., An efficient computation of the angle of latitude, J. Can. Soc. Expl. Geophysicists, 11 (1975), pp. 72–73.Google Scholar
  31. 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.MathSciNetCrossRefGoogle Scholar
  32. 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.MathSciNetGoogle Scholar
  33. 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.MathSciNetzbMATHCrossRefGoogle Scholar
  34. 34.
    Lancaster, P. and Rokne, J.G., Solutions of nonlinear operator equations, SIAM J. Math. Anal., 8 (1977), pp. 448–457. MR 55, 11078.MathSciNetzbMATHCrossRefGoogle Scholar
  35. 35.
    Watkins, D. and Lancaster, P., Some families of finite elements, J. Inst. Math. Appl., 19 (1977), pp. 385–397. MR 55, 11650.MathSciNetzbMATHCrossRefGoogle Scholar
  36. 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.MathSciNetzbMATHCrossRefGoogle Scholar
  37. 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.MathSciNetzbMATHCrossRefGoogle Scholar
  38. 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.MathSciNetGoogle Scholar
  39. 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.MathSciNetzbMATHCrossRefGoogle Scholar
  40. 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.MathSciNetzbMATHCrossRefGoogle Scholar
  41. 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.Google Scholar
  42. 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.Google Scholar
  43. 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.MathSciNetzbMATHCrossRefGoogle Scholar
  44. 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.MathSciNetzbMATHCrossRefGoogle Scholar
  45. 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.MathSciNetzbMATHCrossRefGoogle Scholar
  46. 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.MathSciNetzbMATHCrossRefGoogle Scholar
  47. 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.MathSciNetzbMATHCrossRefGoogle Scholar
  48. 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.Google Scholar
  49. 49.
    Lancaster, P. and Salkauskas, K., Surfaces generated by moving least squares methods, Math. Soc. Comp., 37 (1981), pp. 141–158. MR 83c, 65015.MathSciNetzbMATHCrossRefGoogle Scholar
  50. 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.MathSciNetzbMATHCrossRefGoogle Scholar
  51. 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.MathSciNetzbMATHCrossRefGoogle Scholar
  52. 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.MathSciNetzbMATHCrossRefGoogle Scholar
  53. 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.MathSciNetzbMATHCrossRefGoogle Scholar
  54. 54.
    Lancaster, P. and Tismenetsky, M., Inertia characteristics of self-adjoint matrix polynomials, Lin. Alg. and Appl., 52 (1983), pp. 479–496.MathSciNetGoogle Scholar
  55. 55.
    Lancaster, P. and Tismenetsky, M., Some extensions and modifications of classical stability tests for polynomials, Inter. J. Control, 38 (1983), pp. 369–380.MathSciNetzbMATHCrossRefGoogle Scholar
  56. 56.
    Gohberg, I., Lancaster, P. and Rodman, L., A sign-characteristic for selfadjoint meromorphic matrix functions, Applicable Analysis, 16 (1983), pp. 165–185.MathSciNetzbMATHCrossRefGoogle Scholar
  57. 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.CrossRefGoogle Scholar
  58. 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.MathSciNetzbMATHCrossRefGoogle Scholar
  59. 59.
    Lancaster, P. and Rozsa, P., Eigenvectors of H-selfadjoint matrices, Zeitschrift far Ang. Math. and Mech., 64 (1984), pp. 439–441.MathSciNetzbMATHCrossRefGoogle Scholar
  60. 60.
    Lancaster, P. and Maroulas, J., The kernel of the bezoutian for operator polynomials, J. Lin. Mult. Alg., 17 (1985), pp. 181–201.MathSciNetzbMATHCrossRefGoogle Scholar
  61. 61.
    Gohberg, I., Lancaster, P. and Rodman, L., Perturbations of analytic hermitian matrix functions, Applicable Analysis, 20 (1985), pp. 23–48. MR 87d, 15018.MathSciNetzbMATHCrossRefGoogle Scholar
  62. 62.
    Elsner, L. and Lancaster, P., The spectral variation of pencils of matrices, Jour. Computational Math., 3 (1985), pp. 262–274. MR 87j, 15029.MathSciNetzbMATHGoogle Scholar
  63. 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.MathSciNetGoogle Scholar
  64. 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.MathSciNetzbMATHCrossRefGoogle Scholar
  65. 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.MathSciNetzbMATHCrossRefGoogle Scholar
  66. 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.MathSciNetzbMATHCrossRefGoogle Scholar
  67. 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.MathSciNetzbMATHCrossRefGoogle Scholar
  68. 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.MathSciNetzbMATHCrossRefGoogle Scholar
  69. 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.MathSciNetzbMATHCrossRefGoogle Scholar
  70. 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.MathSciNetCrossRefGoogle Scholar
  71. 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.MathSciNetzbMATHCrossRefGoogle Scholar
  72. 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.MathSciNetzbMATHCrossRefGoogle Scholar
  73. 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.MathSciNetzbMATHCrossRefGoogle Scholar
  74. 74.
    Koltracht, I. and Lancaster, P., Generalized Schur parameters and the effects of perturbations, Lin. Alg. and Appl., 105 (1988), 109–129.MathSciNetzbMATHCrossRefGoogle Scholar
  75. 75.
    Koltracht, I. and Lancaster, P., Threshold algorithms for the prediction of reflection coefficients in a layered medium, Geophysics, 53 (1988), 908–919.CrossRefGoogle Scholar
  76. 76.
    Lancaster, P. and Ye, Q., Inverse spectral problems for linear and quadratic matrix pencils, Lin. Alg. and Appl., 107 (1988), 293–309.MathSciNetzbMATHCrossRefGoogle Scholar
  77. 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.MathSciNetzbMATHCrossRefGoogle Scholar
  78. 78.
    Farid, F.O. and Lancaster, P., Spectral properties of diagonally dominant infinite matrices, Part I, Proc. Roy. Soc. Edinburgh, 111A (1989), 301–314.MathSciNetCrossRefGoogle Scholar
  79. 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.MathSciNetzbMATHCrossRefGoogle Scholar
  80. 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.Google Scholar
  81. 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.MathSciNetzbMATHCrossRefGoogle Scholar
  82. 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.MathSciNetzbMATHCrossRefGoogle Scholar
  83. 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.MathSciNetzbMATHCrossRefGoogle Scholar
  84. 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.MathSciNetzbMATHCrossRefGoogle Scholar
  85. 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.MathSciNetzbMATHCrossRefGoogle Scholar
  86. 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.MathSciNetzbMATHCrossRefGoogle Scholar
  87. 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.MathSciNetzbMATHCrossRefGoogle Scholar
  88. 88.
    Barkwell, L. and Lancaster, P., Overdamped and gyroscopic vibrating systems, Jour. of Appl. Mechanics, 59 (1992), 176–181. AMR 45 (5), #47.MathSciNetzbMATHCrossRefGoogle Scholar
  89. 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.MathSciNetzbMATHCrossRefGoogle Scholar
  90. 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.MathSciNetzbMATHCrossRefGoogle Scholar
  91. 91.
    Lancaster, P., and Ye, Q., Definitizable hermitian matrix pencils, Aequationes Mathematicae, 46 (1993), 44–55.MathSciNetzbMATHCrossRefGoogle Scholar
  92. 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.MathSciNetzbMATHCrossRefGoogle Scholar
  93. 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.MathSciNetzbMATHCrossRefGoogle Scholar
  94. 94.
    Lancaster, P., and Ye, Q., Rayleigh-Ritz and Lanczos methods for symmetric matrix pencils, Lin. Alg. and Appl., 185 (1993), 173–201.MathSciNetzbMATHCrossRefGoogle Scholar
  95. 95.
    Lancaster, P., Shkalikov, A., and Ye, Q., Strongly definitizable linear pencils in Hilbert space, Integral Eq. and Op. Theory, 17 (1993), 338–360.MathSciNetzbMATHCrossRefGoogle Scholar
  96. 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.MathSciNetCrossRefGoogle Scholar
  97. 97.
    Lancaster, P. and Shkalikov, A., Damped vibrations of beams and related spectral problems, Canadian Applied Math. Quarterly, 2 (1994), 45–90.MathSciNetzbMATHGoogle Scholar
  98. 98.
    Lancaster, P. and Rodman, L., Invariant neutral subspaces for symmetric and skew real matrix pairs, Canadian Jour. of Math., 46 (1994), 602–618.MathSciNetzbMATHCrossRefGoogle Scholar
  99. 99.
    Lancaster, P., Markus, A.S., and Matsaev, V.I., Definitizable operators and quasihyperbolic operator polynomials, Jour. of Functional Analysis, 131 (1995), 1–28.MathSciNetzbMATHCrossRefGoogle Scholar
  100. 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.MathSciNetzbMATHCrossRefGoogle Scholar
  101. 101.
    Andrew, A.L., Chu, K.-w.E., and Lancaster, P., On numerical solution of nonlinear eigenvalue problems, Computing, 55 (1995), 91–111.MathSciNetzbMATHCrossRefGoogle Scholar
  102. 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.MathSciNetzbMATHCrossRefGoogle Scholar
  103. 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.MathSciNetzbMATHCrossRefGoogle Scholar
  104. 104.
    Dai, H. and Lancaster, P., Linear matrix equations from an inverse problem of vibration theory, Lin. Alg. and Appl., 246 (1996), 31–47.MathSciNetzbMATHCrossRefGoogle Scholar
  105. 105.
    Krupnik, I., Lancaster, P. and Zizler, P., Factorization of selfadjoint matrix polynomials with real spectrum, J. Lin. Mult. Alg., 40 (1996), 327–336.MathSciNetzbMATHCrossRefGoogle Scholar
  106. 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.Google Scholar
  107. 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.Google Scholar
  108. 108.
    Lancaster, P., Markus, A.S. and Matsaev, V.I., Factorization of selfadjoint operator polynomials, Jour. of Operator Theory, 35 (1996), 337–348.MathSciNetzbMATHGoogle Scholar
  109. 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.MathSciNetzbMATHCrossRefGoogle Scholar
  110. 110.
    Dai, H. and Lancaster, P., Numerical methods for finding multiple eigenvalues of matrices depending on parameters, Numerische Math., 76 (1997), 189–208.MathSciNetzbMATHCrossRefGoogle Scholar
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Expositions, Surveys, etc.

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    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.Google Scholar
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    Lancaster, P., What are universities for?, Position paper for the conference of the same title, University of Calgary, 1988.Google Scholar
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    Lancaster, P., Quadratic eigenvalue problems, Linear Alg. and Appl., 150 (1991), 499–506.MathSciNetGoogle Scholar
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    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.MathSciNetzbMATHCrossRefGoogle Scholar
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    Lancaster, P., Spectra and stability of quadratic eigenvalue problems, Proceedings of the International Workshop on the Recent Advances in Applied Mathematics, Kuwait University, 1996.Google Scholar
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    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.CrossRefGoogle Scholar

Copyright information

© Springer Basel AG 2002

Authors and Affiliations

  • I. Gohberg
    • 1
  • H. Langer
    • 2
  1. 1.School of Mathematical Sciences Raymond and Beverly SacklerFaculty of Exact Sciences Tel Aviv UniversityRamat AvivIsrael
  2. 2.MathematikTechnische Universität WienWienAustria

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