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On efficiently computing the eigenvalues of limited-memory quasi-Newton matrices

Jennifer Erway(erwayjb***at***wfu.edu)
Roummel Marcia(rmarcia***at***ucmerced.edu)

Abstract: In this paper, we consider the problem of efficiently computing the eigenvalues of limited-memory quasi-Newton matrices that exhibit a compact formulation. In addition, we produce a compact formula for quasi-Newton matrices generated by any member of the Broyden convex class of updates. Our proposed method makes use of efficient updates to the QR factorization that substantially reduces the cost of computing the eigenvalues after the quasi-Newton matrix is updated. Numerical experiments suggest that the proposed method is able to compute eigenvalues to high accuracy. Applications for this work include modified quasi-Newton methods and trust-region methods for large-scale optimization, the efficient computation of condition numbers and singular values, and sensitivity analysis.

Keywords: Limited-memory quasi-Newton methods, quasi-Newton matrices, eigenvalues, spectral decomposition, QR decomposition

Category 1: Nonlinear Optimization (Other )

Citation: 2014-6, Wake Forest University

Download: [PDF]

Entry Submitted: 07/10/2015
Entry Accepted: 07/11/2015
Entry Last Modified: 07/10/2015

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