Khazal, R. R. Existence and stability of Cholesky Q. I. F. for symmetric linear systems. (English) Zbl 1008.65017 Int. J. Comput. Math. 79, No. 9, 1013-1023 (2002). 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. Reviewer: R.P.Tewarson (Stony Brook) Cited in 2 Documents MSC: 65F05 Direct numerical methods for linear systems and matrix inversion Keywords:Cholesky factorization; symmetric positive definite systems; stability PDF BibTeX XML Cite \textit{R. R. Khazal}, Int. J. Comput. Math. 79, No. 9, 1013--1023 (2002; Zbl 1008.65017) Full Text: DOI References: [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 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.