Direct and inverse eigenvalue problems for diagonal-plus-semiseparable matrices
A special congruence transformation is introduced for computing the eigenvalues of diagonal-plus-semiseparable (DPSS) matrices which allows the evaluation of the characteristic polynomial in linear time and the direct application of a divide and conquer eigenvalue solver to the DPSS matrix without any preliminary reduction. The inverse eigenvalue problem is then solved to reconstruct the symmetric DPSS matrix from its spectrum and some other information. The results are applied for the QR factorization of special Cauchy matrices.
scientific article; zbMATH DE number 2026782