Adaptive Eigenvalue Computations Using Newton's Method on the Grassmann Manifold

DOI10.1137/S0895479899354688zbMath0999.65019MaRDI QIDQ2784382

Lars Eldén, Eva Lundström

Publication date: 23 April 2002

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

zbMATH Keywords

eigenvalueNewton's methodnumerical examplessingular value decompositioneigenvectorinvariant subspaceconjugate gradient methodToeplitz matrixsparse matrixGrassmann manifoldpreconditionerdifferential geometrySylvester equationsignal subspace problemsingular values and vectors

Mathematics Subject Classification ID

Computational methods for sparse matrices (65F50) Numerical computation of eigenvalues and eigenvectors of matrices (65F15) Numerical computation of matrix norms, conditioning, scaling (65F35) Local Riemannian geometry (53B20)

Related Items (10)

Grassmann algorithms for low rank approximation of matrices with missing values ⋮ Optimization on flag manifolds ⋮ Block Newton method and block Rayleigh quotient iteration for computing invariant subspaces of general complex matrices ⋮ Iterative refinement of Schur decompositions ⋮ High-Order Retractions on Matrix Manifolds Using Projected Polynomials ⋮ Two-sided Grassmann-Rayleigh quotient iteration ⋮ Adaptive finite element solution of eigenvalue problems: Balancing of discretization and iteration error ⋮ A time-varying Newton algorithm for adaptive subspace tracking ⋮ A Geometric Newton Method for Oja's Vector Field ⋮ On correction equations and domain decomposition for computing invariant subspaces

Uses Software

• eigs
• svdpack
• JDQZ

This page was built for publication: Adaptive Eigenvalue Computations Using Newton's Method on the Grassmann Manifold