Structure Preserving Algorithm for the Logarithm of Symplectic Matrices

Bahar Arslan

doi:10.36753/mathenot.868902

EN

Structure Preserving Algorithm for the Logarithm of Symplectic Matrices

Abstract

The current algorithms use either the full form or the Schur decomposition of the matrix in the inverse scaling and squaring method to compute the matrix logarithm. The inverse scaling and squaring method consists of two main calculations: taking a square root and evaluating the Padé approximants. In this work, we suggest using the structure preserving iteration as an alternative to Denman-Beavers iteration for taking a square root. Numerical experiments show that while using the structure preserving square root iteration in the inverse scaling and squaring method preserves the Hamiltonian structure of matrix logarithm, Denman-Beavers iteration and Schur decomposition cause a structure loss.

Keywords

Matrix functions, matrix logarithm, symplectic matrix, Hamiltonian matrix, inverse scaling and squaring method

References

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Details

Primary Language

English

Subjects

Mathematical Sciences

Journal Section

Research Article

Authors

Bahar Arslan ^*
0000-0002-7750-4325
Türkiye

Publication Date

September 30, 2021

Submission Date

January 26, 2021

Acceptance Date

April 20, 2021

Published in Issue

Year 2021 Volume: 9 Number: 3

DOI

https://doi.org/10.36753/mathenot.868902

IZ

https://izlik.org/JA43XF44LB

APA

Arslan, B. (2021). Structure Preserving Algorithm for the Logarithm of Symplectic Matrices. Mathematical Sciences and Applications E-Notes, 9(3), 133-141. https://doi.org/10.36753/mathenot.868902

AMA

1.Arslan B. Structure Preserving Algorithm for the Logarithm of Symplectic Matrices. Math. Sci. Appl. E-Notes. 2021;9(3):133-141. doi:10.36753/mathenot.868902

Chicago

Arslan, Bahar. 2021. “Structure Preserving Algorithm for the Logarithm of Symplectic Matrices”. Mathematical Sciences and Applications E-Notes 9 (3): 133-41. https://doi.org/10.36753/mathenot.868902.

EndNote

Arslan B (September 1, 2021) Structure Preserving Algorithm for the Logarithm of Symplectic Matrices. Mathematical Sciences and Applications E-Notes 9 3 133–141.

IEEE

[1]B. Arslan, “Structure Preserving Algorithm for the Logarithm of Symplectic Matrices”, Math. Sci. Appl. E-Notes, vol. 9, no. 3, pp. 133–141, Sept. 2021, doi: 10.36753/mathenot.868902.

ISNAD

Arslan, Bahar. “Structure Preserving Algorithm for the Logarithm of Symplectic Matrices”. Mathematical Sciences and Applications E-Notes 9/3 (September 1, 2021): 133-141. https://doi.org/10.36753/mathenot.868902.

JAMA

1.Arslan B. Structure Preserving Algorithm for the Logarithm of Symplectic Matrices. Math. Sci. Appl. E-Notes. 2021;9:133–141.

MLA

Arslan, Bahar. “Structure Preserving Algorithm for the Logarithm of Symplectic Matrices”. Mathematical Sciences and Applications E-Notes, vol. 9, no. 3, Sept. 2021, pp. 133-41, doi:10.36753/mathenot.868902.

Vancouver

1.Bahar Arslan. Structure Preserving Algorithm for the Logarithm of Symplectic Matrices. Math. Sci. Appl. E-Notes. 2021 Sep. 1;9(3):133-41. doi:10.36753/mathenot.868902