Structured inverse least-squares problem for structured matrices
Bibhas Adhikari, Rafikul Alam
TL;DR
This paper provides a comprehensive solution to the structured inverse least-squares problem for matrices within specific classes, identifying all solutions and characterizing minimal norm solutions under different norms.
Contribution
It offers a complete characterization of solutions to the structured inverse least-squares problem, including conditions for minimal norm solutions and their uniqueness.
Findings
Infinitely many minimal spectral norm solutions exist.
Unique minimal Frobenius norm solution.
Explicit solution formulas for structured inverse least-squares problems.
Abstract
Given a pair of matrices X and B and an appropriate class of structured matrices S, we provide a complete solution of the structured inverse least-squares problem . Indeed, we determine all solutions of the structured inverse least squares problem as well as those solutions which have the smallest norm. We show that there are infinitely many smallest norm solutions of the least squares problem for the spectral norm whereas the smallest norm solution is unique for the Frobenius norm.
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Taxonomy
TopicsMatrix Theory and Algorithms · Sparse and Compressive Sensing Techniques · Advanced Optimization Algorithms Research