{"title":"计算广义同伴矩阵行列式的快速无击穿算法","authors":"Xin Fan, Ji-Teng Jia","doi":"10.1007/s10910-025-01714-z","DOIUrl":null,"url":null,"abstract":"<div><p>In this paper, we consider the determinant evaluation of a generalized comrade matrix based on a novel incomplete block-diagonalization approach which transforms the determinant of the original generalized comrade matrix into the determinants of tridiagonal matrices and comrade matrix with lower-order. Then, a breakdown-free recursive algorithm for computing the determinant of the generalized comrade matrix is proposed. Even though the algorithm is not a symbolic algorithm, it never suffers from breakdown. Furthermore, we propose an explicit formula for the determinant of the generalized comrade matrix with quasi-Toeplitz structure. Some numerical results with simulations in MATLAB implementation are provided to demonstrate the accuracy and effectiveness of the proposed algorithm, and its competitiveness with MATLAB built-in function.</p></div>","PeriodicalId":648,"journal":{"name":"Journal of Mathematical Chemistry","volume":"63 5","pages":"1189 - 1210"},"PeriodicalIF":1.7000,"publicationDate":"2025-03-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Fast breakdown-free algorithm for computing the determinants of a generalized comrade matrix\",\"authors\":\"Xin Fan, Ji-Teng Jia\",\"doi\":\"10.1007/s10910-025-01714-z\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>In this paper, we consider the determinant evaluation of a generalized comrade matrix based on a novel incomplete block-diagonalization approach which transforms the determinant of the original generalized comrade matrix into the determinants of tridiagonal matrices and comrade matrix with lower-order. Then, a breakdown-free recursive algorithm for computing the determinant of the generalized comrade matrix is proposed. Even though the algorithm is not a symbolic algorithm, it never suffers from breakdown. Furthermore, we propose an explicit formula for the determinant of the generalized comrade matrix with quasi-Toeplitz structure. Some numerical results with simulations in MATLAB implementation are provided to demonstrate the accuracy and effectiveness of the proposed algorithm, and its competitiveness with MATLAB built-in function.</p></div>\",\"PeriodicalId\":648,\"journal\":{\"name\":\"Journal of Mathematical Chemistry\",\"volume\":\"63 5\",\"pages\":\"1189 - 1210\"},\"PeriodicalIF\":1.7000,\"publicationDate\":\"2025-03-15\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Journal of Mathematical Chemistry\",\"FirstCategoryId\":\"92\",\"ListUrlMain\":\"https://link.springer.com/article/10.1007/s10910-025-01714-z\",\"RegionNum\":3,\"RegionCategory\":\"化学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q3\",\"JCRName\":\"CHEMISTRY, MULTIDISCIPLINARY\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Mathematical Chemistry","FirstCategoryId":"92","ListUrlMain":"https://link.springer.com/article/10.1007/s10910-025-01714-z","RegionNum":3,"RegionCategory":"化学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"CHEMISTRY, MULTIDISCIPLINARY","Score":null,"Total":0}
Fast breakdown-free algorithm for computing the determinants of a generalized comrade matrix
In this paper, we consider the determinant evaluation of a generalized comrade matrix based on a novel incomplete block-diagonalization approach which transforms the determinant of the original generalized comrade matrix into the determinants of tridiagonal matrices and comrade matrix with lower-order. Then, a breakdown-free recursive algorithm for computing the determinant of the generalized comrade matrix is proposed. Even though the algorithm is not a symbolic algorithm, it never suffers from breakdown. Furthermore, we propose an explicit formula for the determinant of the generalized comrade matrix with quasi-Toeplitz structure. Some numerical results with simulations in MATLAB implementation are provided to demonstrate the accuracy and effectiveness of the proposed algorithm, and its competitiveness with MATLAB built-in function.
期刊介绍：
The Journal of Mathematical Chemistry (JOMC) publishes original, chemically important mathematical results which use non-routine mathematical methodologies often unfamiliar to the usual audience of mainstream experimental and theoretical chemistry journals. Furthermore JOMC publishes papers on novel applications of more familiar mathematical techniques and analyses of chemical problems which indicate the need for new mathematical approaches.
Mathematical chemistry is a truly interdisciplinary subject, a field of rapidly growing importance. As chemistry becomes more and more amenable to mathematically rigorous study, it is likely that chemistry will also become an alert and demanding consumer of new mathematical results. The level of complexity of chemical problems is often very high, and modeling molecular behaviour and chemical reactions does require new mathematical approaches. Chemistry is witnessing an important shift in emphasis: simplistic models are no longer satisfactory, and more detailed mathematical understanding of complex chemical properties and phenomena are required. From theoretical chemistry and quantum chemistry to applied fields such as molecular modeling, drug design, molecular engineering, and the development of supramolecular structures, mathematical chemistry is an important discipline providing both explanations and predictions. JOMC has an important role in advancing chemistry to an era of detailed understanding of molecules and reactions.
求助内容：
应助结果提醒方式：
京公网安备 11010802042870号
