Admissibly Randomized Coordinate Descent Methods for Computing Extreme Eigenpairs of Symmetric Matrices
Authors:
- 23 April 2025
- journal article
- Published by Wiley in Numerical Linear Algebra with Applications
- Vol. 32 (2)
Abstract
For solving symmetric eigenvalue problems of extremely large matrices that cannot be stored in a whole in the computer memory, we propose a class of admissibly randomized coordinate descent methods by minimizing the corresponding Rayleigh quotients. These iteration methods only call of and operate on a column of the matrix at each of their iteration steps, so they require a small computer memory and have a small computational complexity. We analyze the convergence property of these admissibly randomized coordinate descent methods and confirm their implemental effectiveness by numerical experiments.Keywords
This publication has 21 references indexed in Scilit:
- Randomized Kaczmarz iteration methods: Algorithmic extensions and convergence theoryJapan Journal of Industrial and Applied Mathematics, 2023
- The power method and beyondApplied Numerical Mathematics, 2021
- On local quadratic convergence of inexact simplified Jacobi–Davidson method for interior eigenpairs of Hermitian eigenproblemsApplied Mathematics Letters, 2017
- On local quadratic convergence of inexact simplified Jacobi–Davidson methodLinear Algebra and its Applications, 2017
- Randomized algorithms for generalized Hermitian eigenvalue problems with application to computing Karhunen–Loève expansionNumerical Linear Algebra with Applications, 2015
- Coordinate descent algorithmsMathematical Programming, 2015
- Trace optimization and eigenproblems in dimension reduction methodsNumerical Linear Algebra with Applications, 2010
- A geometric theory for preconditioned inverse iteration III: A short and sharp convergence estimate for generalized eigenvalue problemsLinear Algebra and its Applications, 2003
- Asymptotic Convergence of Conjugate Gradient Methods for the Partial Symmetric EigenproblemNumerical Linear Algebra with Applications, 1997
- The method of coordinate overrelaxation for (A??B)x=0Numerische Mathematik, 1974