Publication

EPIC: A PROVABLE ACCELERATED EIGENSOLVER BASED ON PRECONDITIONING AND IMPLICIT CONVEXITY

Nian Shao
2025

Abstract

This paper is concerned with the extraction of the smallest eigenvalue and its corresponding eigenvector of a symmetric positive definite matrix pencil. We reveal implicit convexity of the eigenvalue problem in Euclidean space. A provable accelerated eigensolver based on preconditioning and implicit convexity (EPIC) is proposed. Theoretical analysis shows the acceleration of EPIC with a rate of convergence resembling the conjectured rate of convergence of the well-known locally optimal preconditioned conjugate gradient. Numerical results confirm our theoretical findings of EPIC.

Official source

https://infoscience.epfl.ch/entities/publication/23bbbe75-df44-4a5b-87e0-0120674bfda3

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