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A Cholesky LR algorithm for the positive definite symmetric diagonal-plus-semiseparable eigenproblem. (English) Zbl 1136.65043
Many algorithms are known for solving the symmetric eigenvalue problem. Among others, an orthogonal similarity reduction was recently presented to reduce a symmetric matrix into a diagonal-plus-semiseparable one (denoted DPSS) with free choice of the diagonal. This paper presents an efficient Cholesky LR algorithm to compute the eigenvalues of a positive definite DPSS matrix, preserving the DPSS structure. A useful feature is that the eigenvalues are computed from the smallest to the largest one, so this algorithm looks very suitable for those problems, where only a couple of the smallest eigenvalues are required. Reported numerical results show that the accuracy exhibited by the presented methods looks competitive with analogous LAPACK routines.

MSC:
65F15 Numerical computation of eigenvalues and eigenvectors of matrices
Software:
LAPACK
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