Perturbation Analyses for the Choleskyfactorization with Backward Rounding
نویسنده
چکیده
This paper gives perturbation analyses for the Cholesky factorization A = R T R of a real symmetric positive deenite matrix A, with the form of perturbations we could expect from the equivalent backward error in A resulting from numerically stable computations on nite precision oating point computers. First-order and rigorous perturbation bounds are are obtained. The analyses more accurately reeect the sensitivity of the problem than previous such results. Both numerical results and an analysis show the standard method of pivoting usually improves the condition of the problem. A useful upper bound on the condition of the problem is derived.
منابع مشابه
Perturbation Analyses for the Cholesky Factorization with Backward Rounding Errors
This paper gives perturbation analyses of the Cholesky factorization with the form of perturbations we could expect from the equivalent backward error in A resulting from numerically stable computations. The analyses more accurately reflect the sensitivity of the problem than previous such results. Both numerical results and an analysis show the standard method of symmetric pivoting usually imp...
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