Formulations and theorems of quadratically convergent methods for inverse symmetric eigenvalue problems

• Aishima Kensuke

  Faculty of Computer and Information Sciences, Hosei University

Abstract

Inverse eigenvalue problems arise in a variety of applications, and thus various Newton's methods, which quadratically converge, have been developed both in theory and practice. Among many studies over thirty years, two extremely significant developments are found. Firstly, smooth matrix decompositions have been successfully applied since the 1990s. Secondly, a matrix multiplication based method has been recently proposed. In this paper, such efficient modern solvers are classified in the context of classical Newton's methods according to their mathematical formulations, and then the corresponding convergence theorems and their relationship are surveyed.

Journal

• Nonlinear Theory and Its Applications, IEICE

  Nonlinear Theory and Its Applications, IEICE 11 (3), 303-326, 2020

  The Institute of Electronics, Information and Communication Engineers

Keywords

• inverse eigenvalue problems
• generalized symmetric eigenvalue problems
• Newton's method
• quadratic convergence
• multiple eigenvalues

Details

• CRID: 1390003825195030144
• NII Article ID: 130007868232
• DOI: 10.1587/nolta.11.303
• ISSN: 21854106
• Web Site: https://www.jstage.jst.go.jp/article/nolta/11/3/11_303/_pdf
• Text Lang: en
• Data Source:
  • JaLC
  • Crossref
  • CiNii Articles
  • KAKEN
• Abstract License Flag: Disallowed