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On a fourth-order matrix method for computing polar decomposition

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Abstract

The purpose of this article is to study the construction of a higher-order matrix method for computing polar decomposition of any arbitrary matrix. It is shown analytically that the new method is convergent and possesses fourth order. The results of the paper are illustrated by numerical examples.

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Acknowledgments

The research of the first author (F. Khaksar Haghani) is financially supported by Shahrekord Branch, Islamic Azad University, Shahrekord, Iran.

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Authors and Affiliations

  1. Department of Mathematics, Shahrekord Branch, Islamic Azad University, Shahrekord, Iran

    Farhad Khaksar Haghani & Fazlollah Soleymani

Authors
  1. Farhad Khaksar Haghani
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  2. Fazlollah Soleymani
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Corresponding author

Correspondence to Fazlollah Soleymani.

Additional information

Communicated by Jinyun Yuan.

Appendix

Appendix

1. Here, we give the complete Mathematica code of the iterative method (10) in a symbolic environment so as to obtain the fourth order of convergence (11).

figure c

2. In this sub-section, we present the complete Mathematica code illustrating how to attain (12).

figure d

Interested readers may contact the corresponding author for obtaining further full written Mathematica codes concerning the derivation of the formulas of the paper.

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Haghani, F.K., Soleymani, F. On a fourth-order matrix method for computing polar decomposition. Comp. Appl. Math. 34, 389–399 (2015). https://doi.org/10.1007/s40314-014-0124-0

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  • DOI: https://doi.org/10.1007/s40314-014-0124-0

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