Structure Preserving Algorithm for the Logarithm of Symplectic Matrices
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Tarih
2021
Yazarlar
Dergi Başlığı
Dergi ISSN
Cilt Başlığı
Yayıncı
Murat TOSUN
Erişim Hakkı
info:eu-repo/semantics/openAccess
Özet
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.
Açıklama
Anahtar Kelimeler
Matrix functions, matrix logarithm, symplectic matrix, Hamiltonian matrix, inverse scaling and squaring method
Kaynak
Mathematical Sciences and Applications E-Notes
WoS Q Değeri
Scopus Q Değeri
Cilt
9
Sayı
3
