Nonlinear Eigenvector Methods for Convex Minimization over the Numerical Range

DOI10.1137/18M1234473zbMath1461.65048OpenAlexW3099619126MaRDI QIDQ5146631

Ding Lu

Publication date: 26 January 2021

Published in: SIAM Journal on Matrix Analysis and Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1137/18m1234473

zbMATH Keywords

numerical rangeRayleigh quotientnonlinear eigenvalue problemeigenvector nonlinearitysequential subspace method

Mathematics Subject Classification ID

Numerical computation of eigenvalues and eigenvectors of matrices (65F15) Norms of matrices, numerical range, applications of functional analysis to matrix theory (15A60)

Related Items (1)

Variational Characterization of Monotone Nonlinear Eigenvector Problems and Geometry of Self-Consistent Field Iteration

Uses Software

• JDQR
• PRIMME
• JDQZ
• BEM++
• lobpcg.m

Cites Work

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• PRIMME
• Numerical analysis of nonlinear eigenvalue problems
• A regularity result for the singular values of a transfer matrix and a quadratically convergent algorithm for computing its \(L_{\infty}\)-norm
• Perturbation bounds for the definite generalized eigenvalue problem
• Nonlinear eigenvector algorithms for local optimization in multivariate data analysis
• Convexity of the joint numerical range: Topological and differential geometric viewpoints.
• Detecting a definite Hermitian pair and a hyperbolic or elliptic quadratic eigenvalue problem, and associated nearness problems
• On optimizing the sum of the Rayleigh quotient and the generalized Rayleigh quotient on the unit sphere
• On computing the generalized Crawford number of a matrix
• The nearest definite pair for the Hermitian generalized eigenvalue problem
• Toward the Optimal Preconditioned Eigensolver: Locally Optimal Block Preconditioned Conjugate Gradient Method
• Minimizing a Quadratic Over a Sphere
• Numerical Optimization of Eigenvalues of Hermitian Matrix Functions
• Hierarchical Matrices: Algorithms and Analysis
• Numerical Estimation of Coercivity Constants for Boundary Integral Operators in Acoustic Scattering
• A Subspace Method for Large-Scale Eigenvalue Optimization
• Computational chemistry from the perspective of numerical analysis
• Rayleigh Quotient Based Optimization Methods for Eigenvalue Problems
• A Trust Region Direct Constrained Minimization Algorithm for the Kohn–Sham Equation
• Accelerated Line-search and Trust-region Methods
• Second order necessary and sufficient conditions for convex composite NDO
• On Minimizing the Maximum Eigenvalue of a Symmetric Matrix
• On the generalized numerical range
• A Stable Generalized Eigenvalue Problem
• Numerical Determination of the Field of Values of a General Complex Matrix
• Templates for the Solution of Algebraic Eigenvalue Problems
• Robust Rayleigh Quotient Minimization and Nonlinear Eigenvalue Problems
• Subspace Acceleration for the Crawford Number and Related Eigenvalue Optimization Problems
• Randomized Algorithms for Optimal Solutions of Double-Sided QCQP With Applications in Signal Processing
• Transmit beamforming for physical-layer multicasting
• Convexity of the Joint Numerical Range
• Solving Boundary Integral Problems with BEM++

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