The least squares and line search in extracting eigenpairs in Jacobi-Davidson method

DOI10.1007/s10543-020-00806-3zbMath1455.65057OpenAlexW3025486464MaRDI QIDQ2216482

Arindama Singh, Mashetti Ravibabu

Publication date: 16 December 2020

Published in: BIT (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10543-020-00806-3

zbMATH Keywords

least squares problemJacobi-Davidson methodline search methodRayleigh-Ritz projection

Mathematics Subject Classification ID

Numerical computation of eigenvalues and eigenvectors of matrices (65F15) Eigenvalues, singular values, and eigenvectors (15A18) Norms of matrices, numerical range, applications of functional analysis to matrix theory (15A60)

Uses Software

• MatrixMarket
• JDQR
• JDQZ

Cites Work

• On refined Ritz vectors and polynomial characterization
• On the correction equation of the Jacobi-Davidson method
• A new variant of Arnoldi method for approximation of eigenpairs
• On the convergence of the Rayleigh quotient iteration for the computation of the characteristic roots and vectors. III: Generalized Rayleigh quotient and characteristic roots with linear elementary divisors. IV: Generalized Rayleigh quotient for nonlinear elementary divisors
• Computing interior eigenvalues of large matrices
• Some theoretical comparisons of refined Ritz vectors and Ritz vectors
• A refined Jacobi-Davidson method and its correction equation
• An analysis of the Rayleigh--Ritz method for approximating eigenspaces
• Matrix Algorithms
• Alternative correction equations in the Jacobi-Davidson method
• Interpolation-Restart Strategies for Resilient Eigensolvers
• Increasing the Performance of the Jacobi--Davidson Method by Blocking
• Controlling Inner Iterations in the Jacobi–Davidson Method
• The Jacobi-Davidson method
• Jacobi Correction Equation, Line Search, and Conjugate Gradients in Hermitian Eigenvalue Computation I: Computing an Extreme Eigenvalue
• Jacobi--Davidson Style QR and QZ Algorithms for the Reduction of Matrix Pencils
• A Jacobi--Davidson Iteration Method for Linear Eigenvalue Problems
• The convergence of harmonic Ritz values, harmonic Ritz vectors and refined harmonic Ritz vectors
• Harmonic projection methods for large non-symmetric eigenvalue problems
• A generalization of Saad's theorem on Rayleigh-Ritz approximations

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