Naslov
Componentwise analysis of direct factorization of real symmetric and Hermitian matrices

Autori
Slapničar, Ivan

Izvornik
Linear algebra and its applications (0024-3795) 272 (1998), 01-03;

Vrsta, podvrsta i kategorija rada
Radovi u časopisima, članak, znanstveni

Ključne riječi
indefinite Cholesky factorization; symmetric matrix; component error bounds

Sažetak
We derive componentwise backward error bound for the factorization $H=GJG^T$, where $H$ is a real symmetric matrix, $G$ has full column rank, and $J$ is diagonal with $\pm 1$'s on the diagonal. We also derive componentwise forward error bound, that is we bound the difference between the exact and the computed factor $G$, in the cases where such bound is possible. We extend these results to the Hermitian case, and to the well-known Bunch--Parlett factorization. Finally, we prove bounds for the scaled condition of the matrix $G$, and show that the factorization can have rank revealing property.

Izvorni jezik
Engleski

Znanstvena područja
Matematika

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