{"title":"实对称矩阵特征方程的牛顿迭代法","authors":"R. Militaru","doi":"10.1109/SYNASC.2006.59","DOIUrl":null,"url":null,"abstract":"The present paper studies the numerical computation of the extreme eigenvalues of a n times n real symmetric matrix A, by the means of the Newton's approximate method for the characteristic polynomial PA(lambda). An iterative algorithm is also presented involving the computation of a trace of an appropriate matrix, instead of using the evaluation of PA(lambda) and its derivative. Numerical examples solved with this algorithm are to be found within as well","PeriodicalId":309740,"journal":{"name":"2006 Eighth International Symposium on Symbolic and Numeric Algorithms for Scientific Computing","volume":null,"pages":null},"PeriodicalIF":0.0000,"publicationDate":"2006-09-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"1","resultStr":"{\"title\":\"On the Newton's Iterative Method for the Characteristic Equation of a Real Symmetric Matrix\",\"authors\":\"R. Militaru\",\"doi\":\"10.1109/SYNASC.2006.59\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"The present paper studies the numerical computation of the extreme eigenvalues of a n times n real symmetric matrix A, by the means of the Newton's approximate method for the characteristic polynomial PA(lambda). An iterative algorithm is also presented involving the computation of a trace of an appropriate matrix, instead of using the evaluation of PA(lambda) and its derivative. Numerical examples solved with this algorithm are to be found within as well\",\"PeriodicalId\":309740,\"journal\":{\"name\":\"2006 Eighth International Symposium on Symbolic and Numeric Algorithms for Scientific Computing\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2006-09-26\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"1\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"2006 Eighth International Symposium on Symbolic and Numeric Algorithms for Scientific Computing\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1109/SYNASC.2006.59\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"2006 Eighth International Symposium on Symbolic and Numeric Algorithms for Scientific Computing","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1109/SYNASC.2006.59","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
On the Newton's Iterative Method for the Characteristic Equation of a Real Symmetric Matrix
The present paper studies the numerical computation of the extreme eigenvalues of a n times n real symmetric matrix A, by the means of the Newton's approximate method for the characteristic polynomial PA(lambda). An iterative algorithm is also presented involving the computation of a trace of an appropriate matrix, instead of using the evaluation of PA(lambda) and its derivative. Numerical examples solved with this algorithm are to be found within as well
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