Naslov
Approximate eigenvectors as preconditioner

Autori
Drmač, Zlatko ; Veselić, Krešimir

Izvornik
Linear Algebra and Its Applications (0024-3795) 309 (2000); 191-215

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

Ključne riječi
Eigenvectors; eigenvalues; preconditioners

Sažetak
Given approximate eigenvector matrix of a Hermitian nonsingular matrix H, the spectral decomposition of H can be obtained by computing H´=*H and then diagonalizing H´. This work addresses the issue of numerical stability of the transition from H to H´ in finite precision arithmetic. Our analysis shows that the eigenvalues will be computed with small relative error if (i) the approximate eigenvectors are sufficiently orthonormal and (ii) the matrix ||||H´||||= is of the form DAD with diagonal D and well-conditioned A. In that case, H´ can be efficiently and accurately diagonalized by the Jacobi method. If is computed by fast eigensolver based on tridiagonalization, this procedure usually gives the eigensolution with high relative accuracy and it is more efficient than accurate Jacobi type methods on their own.

Izvorni jezik
Engleski

Znanstvena područja
Matematika

POVEZANOST RADA