Relationship between accuracy of singular value decomposition and
distribution of singular values

Drozdov Igor Yurievich; Parfenov Denis Vasilevich

Relationship between accuracy of singular value decomposition and distribution of singular values

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: 2023, vol. 27, issue 1, pp. 5–16

Download full text (In Russian)

Abstract

Using numerical experiments we demonstrated that accuracy of numerical singular value decomposition (SVD) is aﬀected not only by condition number of the matrix, but also by distribution of singular values in the matrix spectrum. We note that widely used relative norm error of SVD result might be insufficient and propose an alternative metric based on root-mean-squared relative error.

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

BibTeX

@article{IS-Drozdov-Parfenov2023,
  author  = {Drozdov, Igor Yurievich and Parfenov, Denis Vasilevich},
  title   = {{Relationship between accuracy of singular value decomposition and distribution of singular values}},
  journal = {Intelligent Systems. Theory and Applications},
  year    = {2023},
  volume  = {27},
  number  = {1},
  pages   = {5--16},
}

AMSBIB

\Bibitem{IS-Drozdov-Parfenov2023}
\by I.\,Y.~Drozdov, D.\,V.~Parfenov
\paper Relationship between accuracy of singular value decomposition and distribution of singular values
\jour Intelligent Systems. Theory and Applications
\yr 2023
\vol 27
\issue 1
\pages 5--16
\lang In Russian

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

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