Refined Error Analyses of Cholesky Factorization
Jean Meinguet · SIAM Journal on Numerical Analysis · 1983
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.