矩阵多项式数值范围边界的数值逼近

Applied Numerical Analysis & Computational Mathematics Pub Date : 2005-04-12 DOI:10.1002/anac.200410029

P. Psarrakos, Ch. Tsitouras

{"title":"矩阵多项式数值范围边界的数值逼近","authors":"P. Psarrakos, Ch. Tsitouras","doi":"10.1002/anac.200410029","DOIUrl":null,"url":null,"abstract":"The numerical range of an n × n matrix polynomial P(λ) = Amλm + Am–1λm–1 + … + A1λ + A0 is defined by W(P) = {λ ∈ ℂ : x*P(λ)x = 0, x ∈ ℂn, x*x = 1}, and plays an important role in the study of matrix polynomials. In this paper, we describe a methodology for the illustration of its boundary, ∂W(P), using recent theoretical results on numerical ranges and algebraic curves. (© 2005 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)","PeriodicalId":100108,"journal":{"name":"Applied Numerical Analysis & Computational Mathematics","volume":"2 1","pages":"126-133"},"PeriodicalIF":0.0000,"publicationDate":"2005-04-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1002/anac.200410029","citationCount":"3","resultStr":"{\"title\":\"Numerical approximation of the boundary of numerical range of matrix polynomials\",\"authors\":\"P. Psarrakos, Ch. Tsitouras\",\"doi\":\"10.1002/anac.200410029\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"The numerical range of an n × n matrix polynomial P(λ) = Amλm + Am–1λm–1 + … + A1λ + A0 is defined by W(P) = {λ ∈ ℂ : x*P(λ)x = 0, x ∈ ℂn, x*x = 1}, and plays an important role in the study of matrix polynomials. In this paper, we describe a methodology for the illustration of its boundary, ∂W(P), using recent theoretical results on numerical ranges and algebraic curves. (© 2005 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)\",\"PeriodicalId\":100108,\"journal\":{\"name\":\"Applied Numerical Analysis & Computational Mathematics\",\"volume\":\"2 1\",\"pages\":\"126-133\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2005-04-12\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"https://sci-hub-pdf.com/10.1002/anac.200410029\",\"citationCount\":\"3\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Applied Numerical Analysis & Computational Mathematics\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://onlinelibrary.wiley.com/doi/10.1002/anac.200410029\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Applied Numerical Analysis & Computational Mathematics","FirstCategoryId":"1085","ListUrlMain":"https://onlinelibrary.wiley.com/doi/10.1002/anac.200410029","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}

引用次数: 3

摘要

n × n矩阵多项式P(λ) = Amλm + Am-1λm-1 +…+ A1λ + A0的数值范围由W(P) = {λ∈:x*P(λ)x = 0, x∈n, x*x = 1}定义，在矩阵多项式的研究中起着重要作用。在本文中，我们描述了一种方法来说明它的边界，∂W(P)，使用最新的数值范围和代数曲线的理论结果。(©2005 WILEY-VCH Verlag GmbH &KGaA公司，Weinheim)

本文章由计算机程序翻译，如有差异，请以英文原文为准。

查看原文本刊更多论文

Numerical approximation of the boundary of numerical range of matrix polynomials

The numerical range of an n × n matrix polynomial P(λ) = A_mλ^m + A_m–1λ^m–1 + … + A₁λ + A₀ is defined by W(P) = {λ ∈ ℂ : x*P(λ)x = 0, x ∈ ℂⁿ, x*x = 1}, and plays an important role in the study of matrix polynomials. In this paper, we describe a methodology for the illustration of its boundary, ∂W(P), using recent theoretical results on numerical ranges and algebraic curves. (© 2005 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)

求助全文

通过发布文献求助，成功后即可免费获取论文全文。去求助

来源期刊

Applied Numerical Analysis & Computational Mathematics

自引率

0.00%

发文量