Samar, Mahvish; Farooq, Aamir; Mu, Chun-lai Structured condition numbers and statistical condition estimation for the \(LDU\) factorization. (English) Zbl 1474.65104 Appl. Math., Ser. B (Engl. Ed.) 35, No. 3, 332-348 (2020). Summary: In this article, we consider the structured condition numbers for \(LDU\) factorization by using the modified matrix-vector approach and the differential calculus, which can be represented by sets of parameters. By setting the specific norms and weight parameters, we present the expressions of the structured normwise, mixed, componentwise condition numbers and the corresponding results for unstructured ones. In addition, we investigate the statistical estimation of condition numbers of \(LDU\) factorization using the probabilistic spectral norm estimator and the small-sample statistical condition estimation method, and devise three algorithms. Finally, we compare the structured condition numbers with the corresponding unstructured ones in numerical experiments. Cited in 2 Documents MSC: 65F35 Numerical computation of matrix norms, conditioning, scaling 15A23 Factorization of matrices Keywords:\(LDU\) factorization; structured condition number; normwise condition number; mixed condition number; componentwise condition number PDFBibTeX XMLCite \textit{M. Samar} et al., Appl. Math., Ser. B (Engl. Ed.) 35, No. 3, 332--348 (2020; Zbl 1474.65104) Full Text: DOI References: [1] G H Golub, C F Van Loan. Matrix computations, 1996. 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