International Symposium on Nonlinear Theory and its Applications
Accurate Matrix Singular Values
PDF download (57.7KB)
In this paper, an algorithm for accurately calculating singular values of matrices is proposed. The proposed algorithm can treat the cases where the matrices are extremely ill-conditioned, i.e. their condition numbers are allowed to go far beyond the bounds of base precision such as IEEE standard 754 double precision. The algorithm requires standard numerical algorithms, which are commonly implemented in several numerical libraries such as BLAS and LAPACK, and an algorithm for accurate matrix multiplication. Numerical results are presented for illustrating the performance of the proposed algorithm.