{"title":"无界算子分裂的基本方法","authors":"Arieh Iserles , Karolina Kropielnicka","doi":"10.1016/j.camwa.2024.08.031","DOIUrl":null,"url":null,"abstract":"<div><p>Using elementary means, we derive the three most popular splittings of <span><math><msup><mrow><mi>e</mi></mrow><mrow><mi>t</mi><mo>(</mo><mi>A</mi><mo>+</mo><mi>B</mi><mo>)</mo></mrow></msup></math></span> and their error bounds in the case when <em>A</em> and <em>B</em> are (possibly unbounded) operators in a Hilbert space, generating strongly continuous semigroups, <span><math><msup><mrow><mi>e</mi></mrow><mrow><mi>t</mi><mi>A</mi></mrow></msup></math></span>, <span><math><msup><mrow><mi>e</mi></mrow><mrow><mi>t</mi><mi>B</mi></mrow></msup></math></span> and <span><math><msup><mrow><mi>e</mi></mrow><mrow><mi>t</mi><mo>(</mo><mi>A</mi><mo>+</mo><mi>B</mi><mo>)</mo></mrow></msup></math></span>. The error of these splittings is bounded in terms of the norm of the commutators <span><math><mo>[</mo><mi>A</mi><mo>,</mo><mi>B</mi><mo>]</mo></math></span>, <span><math><mo>[</mo><mi>A</mi><mo>,</mo><mo>[</mo><mi>A</mi><mo>,</mo><mi>B</mi><mo>]</mo><mo>]</mo></math></span> and <span><math><mo>[</mo><mi>B</mi><mo>,</mo><mo>[</mo><mi>A</mi><mo>,</mo><mi>B</mi><mo>]</mo><mo>]</mo></math></span>.</p></div>","PeriodicalId":55218,"journal":{"name":"Computers & Mathematics with Applications","volume":null,"pages":null},"PeriodicalIF":2.9000,"publicationDate":"2024-09-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"An elementary approach to splittings of unbounded operators\",\"authors\":\"Arieh Iserles , Karolina Kropielnicka\",\"doi\":\"10.1016/j.camwa.2024.08.031\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>Using elementary means, we derive the three most popular splittings of <span><math><msup><mrow><mi>e</mi></mrow><mrow><mi>t</mi><mo>(</mo><mi>A</mi><mo>+</mo><mi>B</mi><mo>)</mo></mrow></msup></math></span> and their error bounds in the case when <em>A</em> and <em>B</em> are (possibly unbounded) operators in a Hilbert space, generating strongly continuous semigroups, <span><math><msup><mrow><mi>e</mi></mrow><mrow><mi>t</mi><mi>A</mi></mrow></msup></math></span>, <span><math><msup><mrow><mi>e</mi></mrow><mrow><mi>t</mi><mi>B</mi></mrow></msup></math></span> and <span><math><msup><mrow><mi>e</mi></mrow><mrow><mi>t</mi><mo>(</mo><mi>A</mi><mo>+</mo><mi>B</mi><mo>)</mo></mrow></msup></math></span>. The error of these splittings is bounded in terms of the norm of the commutators <span><math><mo>[</mo><mi>A</mi><mo>,</mo><mi>B</mi><mo>]</mo></math></span>, <span><math><mo>[</mo><mi>A</mi><mo>,</mo><mo>[</mo><mi>A</mi><mo>,</mo><mi>B</mi><mo>]</mo><mo>]</mo></math></span> and <span><math><mo>[</mo><mi>B</mi><mo>,</mo><mo>[</mo><mi>A</mi><mo>,</mo><mi>B</mi><mo>]</mo><mo>]</mo></math></span>.</p></div>\",\"PeriodicalId\":55218,\"journal\":{\"name\":\"Computers & Mathematics with Applications\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":2.9000,\"publicationDate\":\"2024-09-13\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Computers & Mathematics with Applications\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://www.sciencedirect.com/science/article/pii/S0898122124003985\",\"RegionNum\":2,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q1\",\"JCRName\":\"MATHEMATICS, APPLIED\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Computers & Mathematics with Applications","FirstCategoryId":"100","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0898122124003985","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
摘要
当 A 和 B 是希尔伯特空间中的（可能是无界的）算子，产生强连续半群 etA、etB 和 et(A+B) 时，我们利用基本方法推导出 et(A+B) 的三种最常用的分裂及其误差边界。这些分裂的误差以换元 [A,B]、[A,[A,B]] 和 [B,[A,B]] 的规范为界。
An elementary approach to splittings of unbounded operators
Using elementary means, we derive the three most popular splittings of and their error bounds in the case when A and B are (possibly unbounded) operators in a Hilbert space, generating strongly continuous semigroups, , and . The error of these splittings is bounded in terms of the norm of the commutators , and .
期刊介绍：
Computers & Mathematics with Applications provides a medium of exchange for those engaged in fields contributing to building successful simulations for science and engineering using Partial Differential Equations (PDEs).
京公网安备 11010802042870号
京ICP备2023020795号-1
分享
求助内容：
应助结果提醒方式：
扫码关注我们
