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

Drozdov Igor Yurievich; Parfenov Denis Vasilevich

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

Drozdov I. Y., Parfenov D. V.

Drozdov Igor Yurievich

senior lecturer, Russian Technological University (MIREA), Institute of Artificial Intelligence, Department of Higher Mathematics

Parfenov Denis Vasilevich

Ph.D., associate professor, Russian Technological University (MIREA), Institute of Artificial Intelligence, Department of Higher Mathematics

Published: 2024, vol. 28, issue 3, pp. 5–17

Download full text (In Russian)

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.

BibTeX

@article{IS-Drozdov-Parfenov2024,
  author  = {Drozdov, Igor Yurievich and Parfenov, Denis Vasilevich},
  title   = {{Accuracy of algorithms of singular value decomposition for matrices with various spectra}},
  journal = {Intelligent Systems. Theory and Applications},
  year    = {2024},
  volume  = {28},
  number  = {3},
  pages   = {5--17},
}

AMSBIB

\Bibitem{IS-Drozdov-Parfenov2024}
\by I.\,Y.~Drozdov, D.\,V.~Parfenov
\paper Accuracy of algorithms of singular value decomposition for matrices with various spectra
\jour Intelligent Systems. Theory and Applications
\yr 2024
\vol 28
\issue 3
\pages 5--17
\lang In Russian

Published under Creative Commons Attribution 4.0 International (CC BY 4.0)

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