Refined Error Analyses of Cholesky Factorization
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This paper concentrates on the practical Cholesky process for solving positive definite symmetric systems of linear equations in standard floating-point arithmetic. Two self-contained round-off analyses are presented, which lead to novel a posteriors error bounds (of practical use) and to refined a priori results (of more theoretical significance). Unmotivated assumptions are avoided with the aim of being constructive throughout.
Roundoff error, a priori bounds, rounding errors, Direct numerical methods for linear systems and matrix inversion, posteriori bounds, numerical positive definiteness, Cholesky factorization
Roundoff error, a priori bounds, rounding errors, Direct numerical methods for linear systems and matrix inversion, posteriori bounds, numerical positive definiteness, Cholesky factorization
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