Decay bounds for the numerical quasiseparable preservation in matrix functions
| Autor: | Leonardo Robol, Stefano Massei |
|---|---|
| Rok vydání: | 2017 |
| Předmět: |
Pure mathematics
Computation Holomorphic function Decay bounds Exponential decay H-matrices Matrix functions Off-diagonal singular values Quasiseparable matrices Algebra and Number Theory Numerical Analysis Geometry and Topology Discrete Mathematics and Combinatorics 010103 numerical & computational mathematics 01 natural sciences Combinatorics FOS: Mathematics Mathematics - Numerical Analysis 0101 mathematics Decay Bounds Mathematics Spectrum (functional analysis) Block matrix Numerical Analysis (math.NA) Function (mathematics) 010101 applied mathematics Singular value Matrix function Gravitational singularity |
| Zdroj: | Linear Algebra and its Applications. 516:212-242 |
| ISSN: | 0024-3795 |
| Popis: | Given matrices 𝐴 and 𝐵 such that 𝐵 = 𝑓(𝐴), where 𝑓(𝑧) is a holomorphic function, we analyze the relation between the singular values of the off-diagonal submatrices of 𝐴 and 𝐵. We provide a family of bounds which depend on the interplay between the spectrum of the argument 𝐴 and the singularities of the function. In particular, these bounds guarantee the numerical preservation of quasiseparable structures under mild hypotheses. We extend the Dunford-Cauchy integral formula to the case in which some poles are contained inside the contour of integration. We use this tool together with the technology of hierarchical matrices (H-matrices) for the effective computation of matrix functions with quasiseparable arguments. ispartof: Linear Algebra and Its Applications vol:516 pages:212-242 status: published |
| Databáze: | OpenAIRE |
| Externí odkaz: |
|
Full Text from ScienceDirect