{"title":"非线性方程系统最优四阶收敛的类似牛顿的两点法","authors":"Harmandeep Singh , Janak Raj Sharma","doi":"10.1016/j.jco.2024.101907","DOIUrl":null,"url":null,"abstract":"<div><div>A two-step Newton-like method is proposed to efficiently solve the systems of nonlinear equations. Extending Newton scheme to a next step as weighted-Newton iteration, the proposed iteration scheme shows optimal fourth order of convergence. The primary objective in formulating the method is to keep the computational efficiency as high as possible. In this context, the efficiency analysis is thoroughly examined using a systematic approach, wherein the efficiency index of the new method is compared with those of existing methods of comparable complexity. Numerical experimentation is performed to investigate the computational efficacy of the developed method. Results indicate higher efficiency and numerical precision in comparison to the existing counterparts.</div></div>","PeriodicalId":50227,"journal":{"name":"Journal of Complexity","volume":"86 ","pages":"Article 101907"},"PeriodicalIF":1.8000,"publicationDate":"2024-11-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"A two-point Newton-like method of optimal fourth order convergence for systems of nonlinear equations\",\"authors\":\"Harmandeep Singh , Janak Raj Sharma\",\"doi\":\"10.1016/j.jco.2024.101907\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><div>A two-step Newton-like method is proposed to efficiently solve the systems of nonlinear equations. Extending Newton scheme to a next step as weighted-Newton iteration, the proposed iteration scheme shows optimal fourth order of convergence. The primary objective in formulating the method is to keep the computational efficiency as high as possible. In this context, the efficiency analysis is thoroughly examined using a systematic approach, wherein the efficiency index of the new method is compared with those of existing methods of comparable complexity. Numerical experimentation is performed to investigate the computational efficacy of the developed method. Results indicate higher efficiency and numerical precision in comparison to the existing counterparts.</div></div>\",\"PeriodicalId\":50227,\"journal\":{\"name\":\"Journal of Complexity\",\"volume\":\"86 \",\"pages\":\"Article 101907\"},\"PeriodicalIF\":1.8000,\"publicationDate\":\"2024-11-05\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Journal of Complexity\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://www.sciencedirect.com/science/article/pii/S0885064X24000840\",\"RegionNum\":2,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q1\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Complexity","FirstCategoryId":"100","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0885064X24000840","RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS","Score":null,"Total":0}
A two-point Newton-like method of optimal fourth order convergence for systems of nonlinear equations
A two-step Newton-like method is proposed to efficiently solve the systems of nonlinear equations. Extending Newton scheme to a next step as weighted-Newton iteration, the proposed iteration scheme shows optimal fourth order of convergence. The primary objective in formulating the method is to keep the computational efficiency as high as possible. In this context, the efficiency analysis is thoroughly examined using a systematic approach, wherein the efficiency index of the new method is compared with those of existing methods of comparable complexity. Numerical experimentation is performed to investigate the computational efficacy of the developed method. Results indicate higher efficiency and numerical precision in comparison to the existing counterparts.
期刊介绍:
The multidisciplinary Journal of Complexity publishes original research papers that contain substantial mathematical results on complexity as broadly conceived. Outstanding review papers will also be published. In the area of computational complexity, the focus is on complexity over the reals, with the emphasis on lower bounds and optimal algorithms. The Journal of Complexity also publishes articles that provide major new algorithms or make important progress on upper bounds. Other models of computation, such as the Turing machine model, are also of interest. Computational complexity results in a wide variety of areas are solicited.
Areas Include:
• Approximation theory
• Biomedical computing
• Compressed computing and sensing
• Computational finance
• Computational number theory
• Computational stochastics
• Control theory
• Cryptography
• Design of experiments
• Differential equations
• Discrete problems
• Distributed and parallel computation
• High and infinite-dimensional problems
• Information-based complexity
• Inverse and ill-posed problems
• Machine learning
• Markov chain Monte Carlo
• Monte Carlo and quasi-Monte Carlo
• Multivariate integration and approximation
• Noisy data
• Nonlinear and algebraic equations
• Numerical analysis
• Operator equations
• Optimization
• Quantum computing
• Scientific computation
• Tractability of multivariate problems
• Vision and image understanding.