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Existence and stability of Cholesky Q. I. F. for symmetric linear systems. (English) Zbl 1008.65017
The question of existence and stability of a variant of the classical Cholesky factorization for the solution of symmetric linear positive definite system of equations proposed by D. J. Evans [ibid. 72, No. 3, 283-288 (1999; Zbl 0949.65023)] is given. Use is made of the fact that the diagonal elements of the factor matrices can be obtained in closed form in terms of certain principal minors of the coefficient matrix. Since the elimination are carried out, alternately, in columns from the left and the right, it is shown that the method is strongly stable if the coefficient matrix is symmetric and positive definite. The operation counts for the new method are shown to agree with those for the classical Cholesky factorization.

MSC:
65F05 Direct numerical methods for linear systems and matrix inversion
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[1] DOI: 10.1080/00207169908804852 · Zbl 0949.65023 · doi:10.1080/00207169908804852
[2] Evans D.J., Parallel Processing Systems pp 357– (1982)
[3] DOI: 10.1080/00207169808804666 · Zbl 0901.65015 · doi:10.1080/00207169808804666
[4] Fox L., An Introduction to Numerical Linear Algebra (1964) · Zbl 0122.35701
[5] Wendroff B., Theoretical Numerical Analysis (1966) · Zbl 0141.32805
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