Part 1. General problems of the intellectual systems theory

Accuracy of algorithms of singular value decomposition for matrices with various spectra

I. Yu. Drozdov, D. V. Parfenov

Artificial Intelligence Institute, MIREA, Moscow

Abstract: We continue to develop our new approach of treating singular spectrum of a matrix as a probability density function to investigate dependencies between accuracy of numerical computation of singular values and spectrum. We conduct massive numerical experiments to demonstrate such dependencies in our new suggested metrics: root-mean-square relative error and median. We present illustrative plots of such dependencies and analyze conclusiveness of these metrics.

Keywords: singular value decomposition, SVD, condition number, matrix spectrum, numerical stability