Structured inverse least-squares problem for structured matrices

2015/01/10 by Bibhas Adhikari, Adhikari, Bibhas, Rafikul Alam +1
Computer Science · Engineering · Mathematics · #Advanced Optimization Algorithms Research #FOS: Mathematics #Matrix Theory and Algorithms #Numerical Analysis (math.NA) #Sparse and Compressive Sensing Techniques

paper · pdf · doi:10.48550/arxiv.1501.02353

openalex publication_date 2015/01/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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 min_A∈S ‖AX-B‖_F. 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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