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Forward stable eigenvalue decomposition of rank-one modifications of diagonal matrices (CROSBI ID 221330)

Prilog u časopisu | izvorni znanstveni rad | međunarodna recenzija

Jakovčević Stor, Nevena ; Slapničar, Ivan ; Barlow, Jesse L. Forward stable eigenvalue decomposition of rank-one modifications of diagonal matrices // Linear algebra and its applications, 487 (2015), 301-315. doi: 10.1016/j.laa.2015.09.025

Podaci o odgovornosti

Jakovčević Stor, Nevena ; Slapničar, Ivan ; Barlow, Jesse L.

engleski

Forward stable eigenvalue decomposition of rank-one modifications of diagonal matrices

We present a new algorithm for solving an eigenvalue problem for a real symmetric matrix which is a rank-one modification of a diagonal matrix. The algorithm computes each eigenvalue and all components of the corresponding eigenvector with high relative accuracy in O(n) operations. The algorithm is based on a shift-and-invert approach. Only a single element of the inverse of the shifted matrix eventually needs to be computed with double the working precision. Each eigenvalue and the corresponding eigenvector can be computed separately, which makes the algorithm adaptable for parallel computing. Our results extend to the complex Hermitian case. The algorithm is similar to the algorithm for solving the eigenvalue problem for real symmetric arrowhead matrices from N. Jakovčević Stor et al. (2015) [16].

Eigenvalue decomposition ; Diagonal-plus-rank-one matrix ; Real symmetric matrix ; Arrowhead matrix ; High relative accuracy ; Forward stability

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Podaci o izdanju

487

2015.

301-315

objavljeno

0024-3795

10.1016/j.laa.2015.09.025

Povezanost rada

Matematika

Poveznice
Indeksiranost