High-relative-accuracy computations with Kac-Murdock-Szegö matrices and their generalizations
Jorge Delgado, Juan Manuel Peña · Computational and Applied Mathematics · 2025
Abstract A linear-time-complexity method to obtain the bidiagonal decomposition of a generalized Kac-Murdock-Szegö matrix is presented. For convenient values of the parameters, it can be obtained with high relative accuracy and it can be also used to compute all eigenvalues, all singular values, the inverse and the solution of some linear systems of equations with high relative accuracy.