Naslov
Accurate eigenvalue decomposition of rank-one modifications of diagonal matrices

Autori
Jakovčević Stor, Nevena ; Slapničar, Ivan

Vrsta, podvrsta i kategorija rada
Sažeci sa skupova, sažetak, znanstveni

Izvornik
Conference on Applied Mathematics and Scientific Computing / - , 2013

Skup
8th Conference on Applied Mathematics and Scientific Computing

Mjesto i datum
Šibenik, Hrvatska, 10.07.2013. - 14.07.2013

Vrsta sudjelovanja
Predavanje

Vrsta recenzije
Međunarodna recenzija

Ključne riječi
eigenvalue decomposition; rank-one modifications of diagonal matrices

Sažetak
We present a new algorithm for solving an eigenvalue problem for a real symmetric matrix which is a rank-one modificiation of a diagonal matrix. The algorithm computes all eigenvalues and all components of the corresponding eigenvectors with high relative accuracy in O(n2) 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 of 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 Hermitian case. The method can be used as a part of divide-and-conquer method for real symmetric tridiagonal matrices.

Izvorni jezik
Engleski

Znanstvena područja
Matematika

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