Sparse pseudoinverses via LP and SDP relaxations of Moore-Penrose
Provides computationally efficient sparse pseudoinverses for handling over- and under-determined systems, benefiting applications in signal processing and machine learning.
The paper introduces new sparse pseudoinverses using LP and SDP relaxations of Moore-Penrose properties, achieving sparser solutions than existing methods.
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.