Structured mapping problems for linearly structured matrices
Bibhas Adhikari, Rafikul Alam
TL;DR
This paper characterizes structured matrices that solve linear mapping problems, explores minimal norm solutions, and applies these findings to structured backward errors, pseudospectra, and invariant subspaces.
Contribution
It provides a comprehensive characterization of structured matrices solving linear equations and analyzes their properties related to eigenvalues and pseudospectra.
Findings
Characterized matrices X and B for structured matrix A solving AX=B
Identified all structured matrices with minimal norm solving the problem
Applied results to structured backward errors and pseudospectra analysis
Abstract
Given an appropriate class of structured matrices S; we characterize matrices X and B for which there exists a matrix A \in S such that AX = B and determine all matrices in S mapping X to B. We also determine all matrices in S mapping X to B and having the smallest norm. We use these results to investigate structured backward errors of approximate eigenpairs and approximate invariant subspaces, and structured pseudospectra of structured matrices.
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