Accurate eigenvalue decomposition of rank-one modifications of diagonal matrices (CROSBI ID 635060)
Prilog sa skupa u zborniku | sažetak izlaganja sa skupa | međunarodna recenzija
Podaci o odgovornosti
Jakovčević Stor, Nevena ; Slapničar, Ivan
engleski
Accurate 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 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.
eigenvalue decomposition; rank-one modifications of diagonal matrices
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Podaci o prilogu
2013.
objavljeno
Podaci o matičnoj publikaciji
Conference on Applied Mathematics and Scientific Computing
Podaci o skupu
8th Conference on Applied Mathematics and Scientific Computing
predavanje
10.07.2013-14.07.2013
Šibenik, Hrvatska