{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T01:34:24Z","timestamp":1760146464692,"version":"build-2065373602"},"reference-count":31,"publisher":"MDPI AG","issue":"11","license":[{"start":{"date-parts":[[2024,11,4]],"date-time":"2024-11-04T00:00:00Z","timestamp":1730678400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Suqian University Youth Foundation","award":["2023XQNA15","K202419"],"award-info":[{"award-number":["2023XQNA15","K202419"]}]},{"name":"Suqian Sci &amp; Tech Program","award":["2023XQNA15","K202419"],"award-info":[{"award-number":["2023XQNA15","K202419"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Axioms"],"abstract":"<jats:p>The study of matrix functions is highly significant and has important applications in control theory, quantum mechanics, signal processing, and machine learning. Previous work has mainly focused on how to use the Krylov-type method to efficiently calculate matrix functions f(A)\u03b2 and \u03b2Tf(A)\u03b2 when A is symmetric. In this paper, we mainly illustrate the convergence using the polynomial approximation theory for the case where A is symmetric positive definite. Numerical results illustrate the effectiveness of our theoretical results.<\/jats:p>","DOI":"10.3390\/axioms13110764","type":"journal-article","created":{"date-parts":[[2024,11,4]],"date-time":"2024-11-04T10:57:20Z","timestamp":1730717840000},"page":"764","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["On the Lanczos Method for Computing Some Matrix Functions"],"prefix":"10.3390","volume":"13","author":[{"given":"Ying","family":"Gu","sequence":"first","affiliation":[{"name":"School of Sciences and Arts, Suqian University, Suqian 223800, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-9277-8092","authenticated-orcid":false,"given":"Hari Mohan","family":"Srivastava","sequence":"additional","affiliation":[{"name":"Department of Mathematics and Statistics, University of Victoria, Victoria, BC V8W 3R4, Canada"},{"name":"Department of Medical Research, China Medical University Hospital, China Medical University, Taichung 40402, Taiwan"},{"name":"Department of Mathematics and Informatics, Azerbaijan University, AZ197 Baku, Azerbaijan"},{"name":"Section of Mathematics, International Telematic University Uninettuno, I-00186 Rome, Italy"},{"name":"Center for Converging Humanities, Kyung Hee University, 26 Kyungheedae-ro, Dongdaemun-gu, Seoul 02447, Republic of Korea"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Xiaolan","family":"Liu","sequence":"additional","affiliation":[{"name":"School of Sciences and Arts, Suqian University, Suqian 223800, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2024,11,4]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"126716","DOI":"10.1016\/j.jmaa.2022.126716","article-title":"Discrete matrix hypergeometric functions","volume":"518","author":"Cuchta","year":"2023","journal-title":"J. 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