{"title":"基于雅可比多项式的核多项式方法","authors":"I.O. Raikov, Y.M. Beltukov","doi":"10.1016/j.amc.2024.129207","DOIUrl":null,"url":null,"abstract":"The kernel polynomial method based on Jacobi polynomials <mml:math altimg=\"si1.svg\"><mml:msubsup><mml:mrow><mml:mi>P</mml:mi></mml:mrow><mml:mrow><mml:mi>n</mml:mi></mml:mrow><mml:mrow><mml:mo stretchy=\"false\">(</mml:mo><mml:mi>α</mml:mi><mml:mo>,</mml:mo><mml:mi>β</mml:mi><mml:mo stretchy=\"false\">)</mml:mo></mml:mrow></mml:msubsup><mml:mo stretchy=\"false\">(</mml:mo><mml:mi>x</mml:mi><mml:mo stretchy=\"false\">)</mml:mo></mml:math> is proposed. The optimal-resolution positivity-preserving kernels and the corresponding damping factors are calculated. The results provide a generalization of the Jackson damping factors for arbitrary Jacobi polynomials. For <mml:math altimg=\"si2.svg\"><mml:mi>α</mml:mi><mml:mo linebreak=\"goodbreak\" linebreakstyle=\"after\">=</mml:mo><mml:mo>±</mml:mo><mml:mn>1</mml:mn><mml:mo stretchy=\"false\">/</mml:mo><mml:mn>2</mml:mn></mml:math>, <mml:math altimg=\"si3.svg\"><mml:mi>β</mml:mi><mml:mo linebreak=\"goodbreak\" linebreakstyle=\"after\">=</mml:mo><mml:mo>±</mml:mo><mml:mn>1</mml:mn><mml:mo stretchy=\"false\">/</mml:mo><mml:mn>2</mml:mn></mml:math> (Chebyshev polynomials of the first to fourth kinds), explicit trigonometric expressions for the damping factors are obtained. The resulting algorithm can be easily introduced into existing implementations of the kernel polynomial method.","PeriodicalId":55496,"journal":{"name":"Applied Mathematics and Computation","volume":"1 1","pages":""},"PeriodicalIF":3.5000,"publicationDate":"2024-11-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"The kernel polynomial method based on Jacobi polynomials\",\"authors\":\"I.O. Raikov, Y.M. Beltukov\",\"doi\":\"10.1016/j.amc.2024.129207\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"The kernel polynomial method based on Jacobi polynomials <mml:math altimg=\\\"si1.svg\\\"><mml:msubsup><mml:mrow><mml:mi>P</mml:mi></mml:mrow><mml:mrow><mml:mi>n</mml:mi></mml:mrow><mml:mrow><mml:mo stretchy=\\\"false\\\">(</mml:mo><mml:mi>α</mml:mi><mml:mo>,</mml:mo><mml:mi>β</mml:mi><mml:mo stretchy=\\\"false\\\">)</mml:mo></mml:mrow></mml:msubsup><mml:mo stretchy=\\\"false\\\">(</mml:mo><mml:mi>x</mml:mi><mml:mo stretchy=\\\"false\\\">)</mml:mo></mml:math> is proposed. The optimal-resolution positivity-preserving kernels and the corresponding damping factors are calculated. The results provide a generalization of the Jackson damping factors for arbitrary Jacobi polynomials. For <mml:math altimg=\\\"si2.svg\\\"><mml:mi>α</mml:mi><mml:mo linebreak=\\\"goodbreak\\\" linebreakstyle=\\\"after\\\">=</mml:mo><mml:mo>±</mml:mo><mml:mn>1</mml:mn><mml:mo stretchy=\\\"false\\\">/</mml:mo><mml:mn>2</mml:mn></mml:math>, <mml:math altimg=\\\"si3.svg\\\"><mml:mi>β</mml:mi><mml:mo linebreak=\\\"goodbreak\\\" linebreakstyle=\\\"after\\\">=</mml:mo><mml:mo>±</mml:mo><mml:mn>1</mml:mn><mml:mo stretchy=\\\"false\\\">/</mml:mo><mml:mn>2</mml:mn></mml:math> (Chebyshev polynomials of the first to fourth kinds), explicit trigonometric expressions for the damping factors are obtained. The resulting algorithm can be easily introduced into existing implementations of the kernel polynomial method.\",\"PeriodicalId\":55496,\"journal\":{\"name\":\"Applied Mathematics and Computation\",\"volume\":\"1 1\",\"pages\":\"\"},\"PeriodicalIF\":3.5000,\"publicationDate\":\"2024-11-22\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Applied Mathematics and Computation\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.1016/j.amc.2024.129207\",\"RegionNum\":2,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q1\",\"JCRName\":\"MATHEMATICS, APPLIED\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Applied Mathematics and Computation","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1016/j.amc.2024.129207","RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}
The kernel polynomial method based on Jacobi polynomials
The kernel polynomial method based on Jacobi polynomials Pn(α,β)(x) is proposed. The optimal-resolution positivity-preserving kernels and the corresponding damping factors are calculated. The results provide a generalization of the Jackson damping factors for arbitrary Jacobi polynomials. For α=±1/2, β=±1/2 (Chebyshev polynomials of the first to fourth kinds), explicit trigonometric expressions for the damping factors are obtained. The resulting algorithm can be easily introduced into existing implementations of the kernel polynomial method.
期刊介绍：
Applied Mathematics and Computation addresses work at the interface between applied mathematics, numerical computation, and applications of systems – oriented ideas to the physical, biological, social, and behavioral sciences, and emphasizes papers of a computational nature focusing on new algorithms, their analysis and numerical results.
In addition to presenting research papers, Applied Mathematics and Computation publishes review articles and single–topics issues.
京公网安备 11010802042870号
京ICP备2023020795号-1
分享
求助内容：
应助结果提醒方式：
扫码关注我们
