Structure Preserving Algorithm for the Logarithm of Symplectic Matrices

Arslan, Bahar

Structure Preserving Algorithm for the Logarithm of Symplectic Matrices

dc.contributor.author	Arslan, Bahar
dc.date.accessioned	2024-11-01T06:11:57Z
dc.date.available	2024-11-01T06:11:57Z
dc.date.issued	2021
dc.department	BTÜ, Mühendislik ve Doğa Bilimleri Fakültesi, Matematik Bölümü
dc.description.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.
dc.identifier	10.36753/mathenot.868902
dc.identifier.doi	10.36753/mathenot.868902
dc.identifier.endpage	141
dc.identifier.issn	21476268
dc.identifier.issue	3
dc.identifier.startpage	133
dc.identifier.uri	https://hdl.handle.net/20.500.12885/2679
dc.identifier.volume	9
dc.institutionauthor	Arslan, Bahar
dc.language.iso	en
dc.publisher	Murat TOSUN
dc.relation.ispartof	Mathematical Sciences and Applications E-Notes
dc.relation.ispartofseries	Mathematical Sciences and Applications E-Notes
dc.relation.publicationcategory	Makale - Uluslararası Hakemli Dergi - Kurum Öğretim Elemanı
dc.rights	info:eu-repo/semantics/openAccess
dc.subject	Matrix functions
dc.subject	matrix logarithm
dc.subject	symplectic matrix
dc.subject	Hamiltonian matrix
dc.subject	inverse scaling and squaring method
dc.title	Structure Preserving Algorithm for the Logarithm of Symplectic Matrices
dc.type	Letter
oaire.citation.issue	3
oaire.citation.volume	9