Linearly Convergent Randomized Iterative Methods for Computing the Pseudoinverse

Robert M. Gower, Peter Richtárik

Research output: Working paper

Abstract

We develop the first stochastic incremental method for calculating the Moore-Penrose pseudoinverse of a real matrix. By leveraging three alternative characterizations of pseudoinverse matrices, we design three methods for calculating the pseudoinverse: two general purpose methods and one specialized to symmetric matrices. The two general purpose methods are proven to converge linearly to the pseudoinverse of any given matrix. For calculating the pseudoinverse of full rank matrices we present two additional specialized methods which enjoy a faster convergence rate than the general purpose methods. We also indicate how to develop randomized methods for calculating approximate range space projections, a much needed tool in inexact Newton type methods or quadratic solvers when linear constraints are present. Finally, we present numerical experiments of our general purpose methods for calculating pseudoinverses and show that our methods greatly outperform the Newton-Schulz method on large dimensional matrices.
Original languageEnglish
PublisherArXiv
Publication statusPublished - 19 Dec 2016

Keywords

  • math.NA
  • 15A09, 15B52, 15A24, 65F10, 65F08, 68W20, 65Y20, 65F20, 68Q25, 68W40, 90C20,
  • G.1.3

Fingerprint Dive into the research topics of 'Linearly Convergent Randomized Iterative Methods for Computing the Pseudoinverse'. Together they form a unique fingerprint.

Cite this