Abstract
In an earlier paper in this series [1] the solution of a system of equations Ax=b with a positive definite matrix of coefficients was described; this was based on the Cholesky factorization of A. If A is ill-conditioned the computed solution may not be sufficiently accurate, but (provided A is not almost singular to working accuracy) it may be improved by an iterative procedure in which the Cholesky decomposition is used repeatedly.
Prepublished in Numer. Math. 8, 203–216 (1966).
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References
Martin, R. S., G. Peters, and J. H. Wilkinson. Symmetric decompositions of a positive definite matrix. Numer. Math. 7, 362–383 (1965). Cf. I/1.
Wilkinson, J. H.: Rounding errors in algebraic processes. London: Her Majesty’s Stationary Office; Englewood Cliffs, N.J.: Prentice-Hall 1963. German edition: Rundungsfehler. Berlin-Göttingen-Heidelberg: Springer 1969.
Wilkinson, J. H The algebraic eigenvalue problem. London: Oxford University Press 1965.
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Martin, R.S., Peters, G., Wilkinson, J.H. (1971). Iterative Refinement of the Solution of a Positive Definite System of Equations. 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_2
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DOI: https://doi.org/10.1007/978-3-642-86940-2_2
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