Abstract
The Interval Buneman Algorithm for Arbitrary Block Dimension. The interval arithmetic Buneman algorithm is a “fast solver” for a class of block tridiagonal systems with interval coefficients. In the present paper, we consider a modification for arbitrary block dimension and we discuss its inclusion properties.
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References
Alefeld, G., Herzberger, J.: Introduction to interval computations. New York: Academic Press 1983.
Barth, W., Nuding, E.: Optimale Lösung von Intervallgleichungssystemen. Computing 12, 117 – 125 (1974).
Buneman, O.: A compact noniterative poisson solver, Institute for Plasma Research Report 294, Stanford University, 1969.
Buzbee, B., Golub, G., Nielson, C.: On direct methods for solving Poisson’s equation. SIAM J. Num. Anal. 7, 627 – 656 (1970).
Frommer, A., Mayer, G.: Parallel interval multisplittings. Numerische Mathematik 56, 255 – 267 (1989).
Kulisch, U., Miranker, W.: Computer arithmetic in theory and practice. New York: Academic Press 1981.
Kulisch, U., Miranker. W.: A new approach to scientific computation. New York: Academic Press 1983.
Mayer, G.: Enclosing the solution of linear systems with inaccurate data by iterative methods based on incomplete LU-decompositions. Computing 35, 189 – 206 (1987).
Neumaier, A.: New techniques for the analysis of linear interval equations. Lin. Alg. Appl. 87, 155 – 179 (1987).
Neumaier, A.: Interval methods for systems of equations. Cambridge: Cambridge University Press 1990.
Schwandt, H.: An interval arithmetic approach for the construction of an almost globally convergent method for the solution of the nonlinear Poisson equation on the unit square. SIAM J. Sci. Stat. Comp. 5, 427 – 452 (1984).
Schwandt, H.: Interval arithmetic for systems of nonlinear equations arising from discretizations of quasilinear elliptic and parabolic partial difTerential equations. Appl. Num. Math. 3, 257 – 287 (1987).
Schwandt, H.: Cyclic reduction for tridiagonal systems of equations with interval coefficients of vector computers, SIAM J. Num. Anal. 26, 661 – 680 (1989).
Swarztrauber, P.: Vector and parallel methods for the direct Solution of Poisson’s equation. J. Comp. Appl. Math. 27, 241 – 263 (1989).
Swarztrauber, P.: The methods of cyclic reduetion, Fourier analysis and the FACR algorithm for the discrete solution of Poisson’s equations on a rectangle. SIAM Review 19, 490 – 501 (1977).
Sweet, R.: A generalized cyclic reduetion algorithm. SIAM J. Num. Anal. 11, 506 – 520 (1974).
Sweet, R.: A cyclic reduetion algorithm for solving block tridiagonal systems of arbitrary dimension. SIAM J. Num. Anal. 14, 706 – 720 (1977).
Varga, R.: Matrix iterative analysis. Englewood Cliffs, New Jersey: Prentice-Hall 1962.
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Dedicated to Professor U. Kulisch on the occasion of his 60th birthday
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© 1993 Springer-Verlag
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Schwandt, H. (1993). The Interval Buneman Algorithm for Arbitrary Block Dimension. In: Albrecht, R., Alefeld, G., Stetter, H.J. (eds) Validation Numerics. Computing Supplementum, vol 9. Springer, Vienna. https://doi.org/10.1007/978-3-7091-6918-6_16
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DOI: https://doi.org/10.1007/978-3-7091-6918-6_16
Publisher Name: Springer, Vienna
Print ISBN: 978-3-211-82451-1
Online ISBN: 978-3-7091-6918-6
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