{"title":"ContHutch++: Stochastic Trace Estimation For Implicit Integral Operators","authors":"Jennifer Zvonek, Andrew J. Horning, Alex Townsend","doi":"10.1137/23m1614365","DOIUrl":null,"url":null,"abstract":"SIAM Journal on Numerical Analysis, Volume 63, Issue 1, Page 334-359, February 2025. <br/> Abstract. Hutchinson’s estimator is a randomized algorithm that computes an [math]-approximation to the trace of any positive semidefinite matrix using [math] matrix-vector products. An improvement of Hutchinson’s estimator, known as [math], only requires [math] matrix-vector products. In this paper, we propose a generalization of [math], which we call [math], that uses operator-function products to efficiently estimate the trace of any trace-class integral operator. Our ContHutch++ estimates avoid spectral artifacts introduced by discretization and are accompanied by rigorous high-probability error bounds. We use ContHutch++ to derive a new high-order accurate algorithm for quantum density-of-states and also show how it can estimate electromagnetic fields induced by incoherent sources.","PeriodicalId":49527,"journal":{"name":"SIAM Journal on Numerical Analysis","volume":"23 1","pages":""},"PeriodicalIF":2.9000,"publicationDate":"2025-02-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"SIAM Journal on Numerical Analysis","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1137/23m1614365","RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}
引用次数: 0
Abstract
SIAM Journal on Numerical Analysis, Volume 63, Issue 1, Page 334-359, February 2025. Abstract. Hutchinson’s estimator is a randomized algorithm that computes an [math]-approximation to the trace of any positive semidefinite matrix using [math] matrix-vector products. An improvement of Hutchinson’s estimator, known as [math], only requires [math] matrix-vector products. In this paper, we propose a generalization of [math], which we call [math], that uses operator-function products to efficiently estimate the trace of any trace-class integral operator. Our ContHutch++ estimates avoid spectral artifacts introduced by discretization and are accompanied by rigorous high-probability error bounds. We use ContHutch++ to derive a new high-order accurate algorithm for quantum density-of-states and also show how it can estimate electromagnetic fields induced by incoherent sources.
期刊介绍：
SIAM Journal on Numerical Analysis (SINUM) contains research articles on the development and analysis of numerical methods. Topics include the rigorous study of convergence of algorithms, their accuracy, their stability, and their computational complexity. Also included are results in mathematical analysis that contribute to algorithm analysis, and computational results that demonstrate algorithm behavior and applicability.
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