Sparse pseudoinverses via LP and SDP relaxations of Moore-Penrose

2016/06/22 by Victor K. Fuentes, Fuentes, Victor K., Marcia Fampa +3 · 2 citations
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.1606.06969

openalex publication_date 2016/06/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01

Abstract

Pseudoinverses are ubiquitous tools for handling over- and under-determined systems of equations. For computational efficiency, sparse pseudoinverses are desirable. Recently, sparse left and right pseudoinverses were introduced, using 1-norm minimization and linear programming. We introduce several new sparse pseudoinverses by developing linear and semi-definite programming relaxations of the well-known Moore-Penrose properties.

Citations

• Semidefinite programming relaxations for semialgebraic problems
• A Drazin inverse for rectangular matrices

Cited by

• On computing sparse universal solvers for key problems in statistics
• On Sparse Reflexive Generalized Inverses

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