Abstract
In an earlier paper in this series [2] the triangular factorization of positive definite band matrices was discussed. With such matrices there is no need for pivoting, but with non-positive definite or unsymmetric matrices pivoting is necessary in general, otherwise severe numerical instability may result even when the matrix is well-conditioned.
Prepublished in Numer. Math. 9, 279–301 (1967).
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References
Bowdler, H. J., R.S. Martin, G. Peters, and J.H. Wilkinson: Solution of Real and Complex Systems of Linear Equations. Numer. Math. 8, 217 – 234 (1966). Cf. I/7.
Martin, R. S., and J. H. Wilkinson: Symmetric decomposition of positive definite band matrices. Numer. Math. 7, 355 – 361 (1965). Cf. I/4.
Martin, R. S., G. Peters, and J. H. Wilkinson: Iterative refinement of the solution of a positive definite system of equations. Numer. Math. 8, 203–216 (1966). Cf. I/2.
Peters, G., and J. H. Wilkinson: The calculation of specified eigenvectors by inverse iteration. Cf. H/18.
Wilkinson, J. H.: The algebraic eigenvalue problem. London: Oxford University Press 1965.
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© 1971 Springer-Verlag Berlin Heidelberg
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Martin, R.S., Wilkinson, J.H. (1971). Solution of Symmetric and Unsymmetric Band Equations and the Calculations of Eigenvectors of Band Matrices. In: Bauer, F.L. (eds) Linear Algebra. Handbook for Automatic Computation, vol 2. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-39778-7_6
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DOI: https://doi.org/10.1007/978-3-662-39778-7_6
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