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.
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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 de-finite band matrices. Numer. Math. 7, 355 -361 (1965). Cf. I/4.
Martin, R. S., and J. H. Wilkinson, 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. 1/2.
Peters, G., and J. H. Wilkinson. The calculation of specified eigenvectors by inverse iteration. Cf. II/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., Householder, A.S., Olver, F.W.J., Rutishauser, H., Samelson, K., Stiefel, E. (eds) Handbook for Automatic Computation. Die Grundlehren der mathematischen Wissenschaften, vol 186. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-86940-2_6
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DOI: https://doi.org/10.1007/978-3-642-86940-2_6
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