Work

Local Convergence Behavior of Extended Local Optimal Block Preconditioned Conjugate Gradient Method for Computing Eigenvalues of Hermitian Matrices

Year: 2026

Type: article

Abstract: ABSTRACT This paper provides a comprehensive and detailed analysis of the local convergence behavior of an extended variation of the locally optimal preconditioned conjugate gradient method (LOBPCG) for computing the extreme eigenvalues of a Hermitian matrix. The convergence rates derived in this work are either obtained for the first time or sharper than those previously established, including those in Ovtchinnikov's work ( SIAM J. Numer. Anal. , 46(5):2567–2592, 2008). The study also extends to generalized problems, including Hermitian matrix polynomials that admit an extended form of the Rayleigh quotient. The new approach used to obtain these rates may also serve as a valuable tool for the convergence analysis of other gradient‐type optimization methods.

Source: Numerical Linear Algebra with Applications

DOI: 10.1002/nla.70075

Authors: Zhechen Shen, Xin Liang

Institutions: Tsinghua University, Beijing Institute of Mathematical Sciences and Applications

Language: English

Topic: Matrix Theory and Algorithms

Subfield: Computational Theory and Mathematics

Field: Computer Science

Domain: Physical Sciences

Open Access status: green

Funder: National Natural Science Foundation of China

Award: G1906853716