On Sparse Reflexive Generalized Inverses

2018/07/09 by Marcia Fampa, Fampa, Marcia, Jon Lee +1 · 1 citation
Computer Science · Engineering · Mathematics · #90C26 90C25 15A09 65K05 #Advanced Optimization Algorithms Research #Computational Complexity (cs.CC) #FOS: Computer and information sciences #FOS: Mathematics #Matrix Theory and Algorithms #Numerical Analysis (math.NA) #Optimization and Control (math.OC) #Sparse and Compressive Sensing Techniques

paper · pdf · doi:10.48550/arxiv.1807.03074

openalex publication_date 2018/07/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study sparse generalized inverses H of a rank-r real matrix A. We give a construction for reflexive generalized inverses having at most r² nonzeros. For r=1 and for r=2 with A nonnegative, we demonstrate how to minimize the (vector) 1-norm over reflexive generalized inverses. For general r, we efficiently find reflexive generalized inverses with 1-norm within approximately a factor of r² of the minimum 1-norm generalized inverse.

Citations

• A generalized inverse for matrices
• Sparse pseudoinverses via LP and SDP relaxations of Moore-Penrose

Cited by

• On computing sparse universal solvers for key problems in statistics

Related

• Approximate 1-norm minimization and minimum-rank structured sparsity for various generalized inverses via local search
• 1-norm minimization and minimum-rank structured sparsity for symmetric and ah-symmetric generalized inverses: rank one and two
• Trading off 1-norm and sparsity against rank for linear models using\n mathematical optimization: 1-norm minimizing partially reflexive ah-symmetric\n generalized inverses
• Good and Fast Row-Sparse ah-Symmetric Reflexive Generalized Inverses
• Experimental analysis of local searches for sparse reflexive generalized inverses