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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.

65F15 Numerical computation of eigenvalues and eigenvectors of matrices
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