Admissibly Randomized Coordinate Descent Methods for Computing Extreme Eigenpairs of Symmetric Matrices
Zhong‐Zhi Bai, Yan‐Qi Chen · Numerical Linear Algebra with Applications · 2025
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.