Accurate eigenvalue decomposition of real symmetric arrowhead matrices and applications (CROSBI ID 191124)
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Podaci o odgovornosti
Jakovčević Stor, Nevena ; Slapničar, Ivan ; Barlow, Jesse L.
engleski
Accurate eigenvalue decomposition of real symmetric arrowhead matrices and applications
We present a new algorithm for solving an eigenvalue problem for a real symmetric arrowhead matrix. The algorithm computes all eigenvalues and all components of the corresponding eigenvectors with high relative accuracy in $O(n^{; ; ; ; ; 2}; ; ; ; ; )$ operations. The algorithm is based on a shift-and-invert approach. Double precision is eventually needed to compute only one element of the inverse of the shifted matrix. Each eigenvalue and the corresponding eigenvector can be computed separately, which makes the algorithm adaptable for parallel computing. Our results extend to Hermitian arrowhead matrices, real symmetric diagonal-plus-rank-one matrices and singular value decomposition of real triangular arrowhead matrices.
eigenvalue decomposition; arrowhead matrix; high relative accuracy; singular value decomposition
Special issue on eigenvalue problems.
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