{"title":"修正Cramer规则及其在求解WZ分解线性系统中的应用","authors":"O. Babarinsa, H. Kamarulhaili","doi":"10.11113/MATEMATIKA.V35.N1.1073","DOIUrl":null,"url":null,"abstract":"The proposed modified methods of Cramer's rule consider the column vector as well as the coefficient matrix concurrently in the linear system. The modified methods can be applied since Cramer's rule is typically known for solving the linear systems in $WZ$ factorization to yield Z-matrix. Then, we presented our results to show that there is no tangible difference in performance time between Cramer's rule and the modified methods in the factorization from improved versions of MATLAB. Additionally, the Frobenius norm of the modified methods in the factorization is better than using Cramer's rule irrespective of the version of MATLAB used.","PeriodicalId":43733,"journal":{"name":"Matematika","volume":null,"pages":null},"PeriodicalIF":0.3000,"publicationDate":"2019-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"1","resultStr":"{\"title\":\"Modified Cramer’s Rule and its Application to Solve Linear Systems in WZ Factorization\",\"authors\":\"O. Babarinsa, H. Kamarulhaili\",\"doi\":\"10.11113/MATEMATIKA.V35.N1.1073\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"The proposed modified methods of Cramer's rule consider the column vector as well as the coefficient matrix concurrently in the linear system. The modified methods can be applied since Cramer's rule is typically known for solving the linear systems in $WZ$ factorization to yield Z-matrix. Then, we presented our results to show that there is no tangible difference in performance time between Cramer's rule and the modified methods in the factorization from improved versions of MATLAB. Additionally, the Frobenius norm of the modified methods in the factorization is better than using Cramer's rule irrespective of the version of MATLAB used.\",\"PeriodicalId\":43733,\"journal\":{\"name\":\"Matematika\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.3000,\"publicationDate\":\"2019-04-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"1\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Matematika\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.11113/MATEMATIKA.V35.N1.1073\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q4\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Matematika","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.11113/MATEMATIKA.V35.N1.1073","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"MATHEMATICS","Score":null,"Total":0}
Modified Cramer’s Rule and its Application to Solve Linear Systems in WZ Factorization
The proposed modified methods of Cramer's rule consider the column vector as well as the coefficient matrix concurrently in the linear system. The modified methods can be applied since Cramer's rule is typically known for solving the linear systems in $WZ$ factorization to yield Z-matrix. Then, we presented our results to show that there is no tangible difference in performance time between Cramer's rule and the modified methods in the factorization from improved versions of MATLAB. Additionally, the Frobenius norm of the modified methods in the factorization is better than using Cramer's rule irrespective of the version of MATLAB used.
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