{"title":"数值半径计算方法的实验比较","authors":"Tim Mitchell , Michael L. Overton","doi":"10.1016/j.rinam.2024.100434","DOIUrl":null,"url":null,"abstract":"<div><p>We make an experimental comparison of methods for computing the numerical radius of an <span><math><mrow><mi>n</mi><mo>×</mo><mi>n</mi></mrow></math></span> complex matrix, based on two well-known characterizations, the first a nonconvex optimization problem in one real variable and the second a convex optimization problem in <span><math><mrow><msup><mrow><mi>n</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>+</mo><mn>1</mn></mrow></math></span> real variables. We make comparisons with respect to both accuracy and computation time using publicly available software.</p></div>","PeriodicalId":36918,"journal":{"name":"Results in Applied Mathematics","volume":"21 ","pages":"Article 100434"},"PeriodicalIF":1.4000,"publicationDate":"2024-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S2590037424000049/pdfft?md5=d346ec67764b480fbb6abfeea3aab6d1&pid=1-s2.0-S2590037424000049-main.pdf","citationCount":"0","resultStr":"{\"title\":\"An experimental comparison of methods for computing the numerical radius\",\"authors\":\"Tim Mitchell , Michael L. Overton\",\"doi\":\"10.1016/j.rinam.2024.100434\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>We make an experimental comparison of methods for computing the numerical radius of an <span><math><mrow><mi>n</mi><mo>×</mo><mi>n</mi></mrow></math></span> complex matrix, based on two well-known characterizations, the first a nonconvex optimization problem in one real variable and the second a convex optimization problem in <span><math><mrow><msup><mrow><mi>n</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>+</mo><mn>1</mn></mrow></math></span> real variables. We make comparisons with respect to both accuracy and computation time using publicly available software.</p></div>\",\"PeriodicalId\":36918,\"journal\":{\"name\":\"Results in Applied Mathematics\",\"volume\":\"21 \",\"pages\":\"Article 100434\"},\"PeriodicalIF\":1.4000,\"publicationDate\":\"2024-02-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"https://www.sciencedirect.com/science/article/pii/S2590037424000049/pdfft?md5=d346ec67764b480fbb6abfeea3aab6d1&pid=1-s2.0-S2590037424000049-main.pdf\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Results in Applied Mathematics\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://www.sciencedirect.com/science/article/pii/S2590037424000049\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"MATHEMATICS, APPLIED\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Results in Applied Mathematics","FirstCategoryId":"1085","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S2590037424000049","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}
An experimental comparison of methods for computing the numerical radius
We make an experimental comparison of methods for computing the numerical radius of an complex matrix, based on two well-known characterizations, the first a nonconvex optimization problem in one real variable and the second a convex optimization problem in real variables. We make comparisons with respect to both accuracy and computation time using publicly available software.
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