Treffer: EPIC: A Provable Accelerated Eigensolver Based on Preconditioning and Implicit Convexity: EPIC: a provable accelerated eigensolver based on preconditioning and implicit convexity
Title:
EPIC: A Provable Accelerated Eigensolver Based on Preconditioning and Implicit Convexity: EPIC: a provable accelerated eigensolver based on preconditioning and implicit convexity
Authors:
Source:
SIAM Journal on Matrix Analysis and Applications. 46:45-73
Publication Status:
Preprint
Publisher Information:
Society for Industrial & Applied Mathematics (SIAM), 2025.
Publication Year:
2025
Subject Terms:
Numerical computation of eigenvalues and eigenvectors of matrices, Convex programming, convexity, preconditioning, FOS: Mathematics, eigenvalue problem, Preconditioners for iterative methods, acceleration, Mathematics - Numerical Analysis, Numerical Analysis (math.NA), 0101 mathematics, 15A08, 65F08, 65F15, 90C25, 01 natural sciences
Document Type:
Fachzeitschrift
Article
File Description:
application/xml
Language:
English
ISSN:
1095-7162
0895-4798
0895-4798
DOI:
10.1137/24m1641440
DOI:
10.48550/arxiv.2401.11786
Access URL:
Rights:
CC BY
Accession Number:
edsair.doi.dedup.....421f4ddf41b1022c4be0cfaf8941aa3d
Database:
OpenAIRE
Weitere Informationen
This paper is concerned with the extraction of the smallest eigenvalue and the 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 the rate of convergence resembling the expected rate of convergence of the well-known locally optimal preconditioned conjugate gradient (LOPCG). A complete proof of the expected rate of convergence of LOPCG is elusive so far. Numerical results confirm our theoretical findings of EPIC.