Newton's method for the parameterized generalized eigenvalue problem with nonsquare matrix pencils

DOI10.1007/s10444-021-09855-wzbMath1465.65029OpenAlexW3153871697MaRDI QIDQ2027787

Mingqing Xiao, Xue-Feng Duan, Wen Li, Jiao-Fen Li

Publication date: 28 May 2021

Published in: Advances in Computational Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10444-021-09855-w

zbMATH Keywords

Newton's methodStiefel manifoldRiemannian optimizationgeneralized eigenvaluenonsquare pencils

Mathematics Subject Classification ID

Numerical computation of eigenvalues and eigenvectors of matrices (65F15) Eigenvalues, singular values, and eigenvectors (15A18)

Related Items (1)

Least-Squares Spectral Methods for ODE Eigenvalue Problems

Uses Software

• Manopt

Cites Work

• Unnamed Item
• Unnamed Item
• A feasible method for optimization with orthogonality constraints
• An Analysis of the Total Least Squares Problem
• A truncated-CG style method for symmetric generalized eigenvalue problems
• Least squares Hermitian solution of the matrix equation \((AXB,CXD)=(E,F)\) with the least norm over the skew field of quaternions
• A matrix-free implementation of Riemannian Newton's method on the Stiefel manifold
• The sign-based methods for solving a class of nonlinear complementarity problems
• A Riemannian conjugate gradient method for optimization on the Stiefel manifold
• Effective algorithms for solving trace minimization problem in multivariate statistics
• A brief introduction to manifold optimization
• Superconvergence of \(C^0-Q^k\) finite element method for elliptic equations with approximated coefficients
• A Riemannian Fletcher--Reeves Conjugate Gradient Method for Doubly Stochastic Inverse Eigenvalue Problems
• An Algorithm for the Generalized Eigenvalue Problem for Nonsquare Matrix Pencils by Minimal Perturbation Approach
• Manopt, a Matlab toolbox for optimization on manifolds
• Generalized Eigenvalues of Nonsquare Pencils with Structure
• Two-Point Step Size Gradient Methods
• The vec-permutation matrix, the vec operator and Kronecker products: a review
• The Geometry of Algorithms with Orthogonality Constraints
• Riemannian Newton-type methods for joint diagonalization on the Stiefel manifold with application to independent component analysis
• On a Generalized Eigenvalue Problem for Nonsquare Pencils
• A Riemannian Optimization Approach to the Matrix Singular Value Decomposition
• An Extrinsic Look at the Riemannian Hessian
• Generalized eigenvalue problems with specified eigenvalues
• The Generalized Eigenvalue Problem for Nonsquare Pencils Using a Minimal Perturbation Approach
• A Geometric Nonlinear Conjugate Gradient Method for Stochastic Inverse Eigenvalue Problems

This page was built for publication: Newton's method for the parameterized generalized eigenvalue problem with nonsquare matrix pencils