Structural analysis of matrix integration operators in polynomial bases

Autor:	F. Rezaei, Robert M. Corless, Amirhossein Amiraslani, M. Hadizadeh
Rok vydání:	2021
Předmět:	Algebra Matrix (mathematics) Polynomial Algebra and Number Theory Basis (linear algebra) Computation Matrix representation Operator theory Integral equation Analysis Sparse matrix Mathematics
Zdroj:	Banach Journal of Mathematical Analysis. 16
ISSN:	1735-8787 2662-2033
DOI:	10.1007/s43037-021-00156-4
Popis:	This work describes a matrix representation approach for efficient and explicit construction of generic well-conditioned matrix integration operators in terms of degree-graded and non-degree-graded polynomial bases. The main advantage of having an explicit formula for an matrix operator in a basis is that we do not need to change the basis given that conversion between bases can occasionally be unstable. We obtain and analyze the matrix integration operators and their structures for some degree-graded polynomial bases, including orthogonal bases, as well as non-degree-graded polynomial bases. The proposed framework may lead to well-structured sparse matrices which can be exploited to reduce the overall complexity in the related matrix computations including matrix–vector multiplications. It appears that applying the idea can be useful to provide an efficient method for functional integral equations.
Databáze:	OpenAIRE
Externí odkaz:	https://explore.openaire.eu/search/publication?articleId=doi_________::c8500fefb67b2ce46b64395ced9470a4 https://doi.org/10.1007/s43037-021-00156-4 Zobrazit plný text záznamu Full text from SpringerLink