Pub Date : 2024-12-06DOI: 10.1016/j.jco.2024.101921
Santhosh George , Muniyasamy M , Manjusree Gopal , Chandhini G , Ioannis K. Argyros
In this paper, we propose a procedure to obtain an iterative method that increases its convergence order from p to 5p for solving nonlinear systems. Our analysis is given in more general Banach space settings and uses assumptions on the derivative of the involved operator only up to order . Here, k is the order of the highest derivative used in the convergence analysis of the iterative method with convergence order p. A particular case of our analysis includes an existing fifth-order method and improves its applicability to more problems than the problems covered by the method's analysis in earlier study.
{"title":"A procedure for increasing the convergence order of iterative methods from p to 5p for solving nonlinear system","authors":"Santhosh George , Muniyasamy M , Manjusree Gopal , Chandhini G , Ioannis K. Argyros","doi":"10.1016/j.jco.2024.101921","DOIUrl":"10.1016/j.jco.2024.101921","url":null,"abstract":"<div><div>In this paper, we propose a procedure to obtain an iterative method that increases its convergence order from <em>p</em> to 5<em>p</em> for solving nonlinear systems. Our analysis is given in more general Banach space settings and uses assumptions on the derivative of the involved operator only up to order <span><math><mi>max</mi><mo></mo><mo>{</mo><mi>k</mi><mo>,</mo><mn>2</mn><mo>}</mo></math></span>. Here, <em>k</em> is the order of the highest derivative used in the convergence analysis of the iterative method with convergence order <em>p</em>. A particular case of our analysis includes an existing fifth-order method and improves its applicability to more problems than the problems covered by the method's analysis in earlier study.</div></div>","PeriodicalId":50227,"journal":{"name":"Journal of Complexity","volume":"87 ","pages":"Article 101921"},"PeriodicalIF":1.8,"publicationDate":"2024-12-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143180612","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-12-04DOI: 10.1016/j.jco.2024.101920
Duo Liu , Qin Huang , Qinian Jin
In recent years, Nesterov acceleration has been introduced to enhance the efficiency of Landweber iteration for solving ill-posed problems. For linear ill-posed problems in Hilbert spaces, Nesterov acceleration has been analyzed with a discrepancy principle proposed to terminate the iterations. However, the existing approach requires computing residuals along two distinct iterative sequences, resulting in increased computational costs. In this paper, we propose an alternative discrepancy principle for Nesterov acceleration that eliminates the need to compute the residuals for one of the iterative sequences, thereby reducing computational time by approximately one-third per iteration. We provide a convergence analysis of the proposed method, establishing both its convergence and convergence rates. The effectiveness of our approach is demonstrated through numerical simulations.
{"title":"A revisit on Nesterov acceleration for linear ill-posed problems","authors":"Duo Liu , Qin Huang , Qinian Jin","doi":"10.1016/j.jco.2024.101920","DOIUrl":"10.1016/j.jco.2024.101920","url":null,"abstract":"<div><div>In recent years, Nesterov acceleration has been introduced to enhance the efficiency of Landweber iteration for solving ill-posed problems. For linear ill-posed problems in Hilbert spaces, Nesterov acceleration has been analyzed with a discrepancy principle proposed to terminate the iterations. However, the existing approach requires computing residuals along two distinct iterative sequences, resulting in increased computational costs. In this paper, we propose an alternative discrepancy principle for Nesterov acceleration that eliminates the need to compute the residuals for one of the iterative sequences, thereby reducing computational time by approximately one-third per iteration. We provide a convergence analysis of the proposed method, establishing both its convergence and convergence rates. The effectiveness of our approach is demonstrated through numerical simulations.</div></div>","PeriodicalId":50227,"journal":{"name":"Journal of Complexity","volume":"87 ","pages":"Article 101920"},"PeriodicalIF":1.8,"publicationDate":"2024-12-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143180615","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-11-29DOI: 10.1016/j.jco.2024.101908
Erich Novak
{"title":"Changes of the Editorial Board","authors":"Erich Novak","doi":"10.1016/j.jco.2024.101908","DOIUrl":"10.1016/j.jco.2024.101908","url":null,"abstract":"","PeriodicalId":50227,"journal":{"name":"Journal of Complexity","volume":"87 ","pages":"Article 101908"},"PeriodicalIF":1.8,"publicationDate":"2024-11-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142745321","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-11-29DOI: 10.1016/j.jco.2024.101919
Luis M. Pardo
{"title":"Succinct obituary in memoriam of Joos Heintz","authors":"Luis M. Pardo","doi":"10.1016/j.jco.2024.101919","DOIUrl":"10.1016/j.jco.2024.101919","url":null,"abstract":"","PeriodicalId":50227,"journal":{"name":"Journal of Complexity","volume":"87 ","pages":"Article 101919"},"PeriodicalIF":1.8,"publicationDate":"2024-11-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142742866","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-11-28DOI: 10.1016/j.jco.2024.101918
Marcelo Actis , Fernando Gaspoz , Pedro Morin , Cornelia Schneider , Nick Schneider
We study direct estimates for adaptive time-stepping finite element methods for time-dependent partial differential equations. Our results generalize previous findings from “On approximation classes for adaptive time-stepping finite element methods” by Actis et al. (2023), where the approximation error was only measured in . In particular, we now also cover the error norms and which are more natural in this context.
{"title":"Direct estimates for adaptive time-stepping finite element methods","authors":"Marcelo Actis , Fernando Gaspoz , Pedro Morin , Cornelia Schneider , Nick Schneider","doi":"10.1016/j.jco.2024.101918","DOIUrl":"10.1016/j.jco.2024.101918","url":null,"abstract":"<div><div>We study direct estimates for adaptive time-stepping finite element methods for time-dependent partial differential equations. Our results generalize previous findings from “On approximation classes for adaptive time-stepping finite element methods” by Actis et al. (2023), where the approximation error was only measured in <span><math><msub><mrow><mi>L</mi></mrow><mrow><mn>2</mn></mrow></msub><mo>(</mo><mo>[</mo><mn>0</mn><mo>,</mo><mi>T</mi><mo>]</mo><mo>,</mo><msub><mrow><mi>L</mi></mrow><mrow><mn>2</mn></mrow></msub><mo>(</mo><mi>Ω</mi><mo>)</mo><mo>)</mo></math></span>. In particular, we now also cover the error norms <span><math><msub><mrow><mi>L</mi></mrow><mrow><mo>∞</mo></mrow></msub><mo>(</mo><mo>[</mo><mn>0</mn><mo>,</mo><mi>T</mi><mo>]</mo><mo>,</mo><msub><mrow><mi>L</mi></mrow><mrow><mn>2</mn></mrow></msub><mo>(</mo><mi>Ω</mi><mo>)</mo><mo>)</mo></math></span> and <span><math><msub><mrow><mi>L</mi></mrow><mrow><mn>2</mn></mrow></msub><mo>(</mo><mo>[</mo><mn>0</mn><mo>,</mo><mi>T</mi><mo>]</mo><mo>,</mo><msup><mrow><mi>H</mi></mrow><mrow><mn>1</mn></mrow></msup><mo>(</mo><mi>Ω</mi><mo>)</mo><mo>)</mo></math></span> which are more natural in this context.</div></div>","PeriodicalId":50227,"journal":{"name":"Journal of Complexity","volume":"87 ","pages":"Article 101918"},"PeriodicalIF":1.8,"publicationDate":"2024-11-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143180611","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-11-05DOI: 10.1016/j.jco.2024.101905
Erich Novak, Mario Ullrich, Jan Vybíral
{"title":"Stefan Heinrich is the Winner of the 2024 Best Paper Award of the Journal of Complexity","authors":"Erich Novak, Mario Ullrich, Jan Vybíral","doi":"10.1016/j.jco.2024.101905","DOIUrl":"10.1016/j.jco.2024.101905","url":null,"abstract":"","PeriodicalId":50227,"journal":{"name":"Journal of Complexity","volume":"86 ","pages":"Article 101905"},"PeriodicalIF":1.8,"publicationDate":"2024-11-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142586490","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-11-05DOI: 10.1016/j.jco.2024.101904
{"title":"Best Paper Award of the Journal of Complexity","authors":"","doi":"10.1016/j.jco.2024.101904","DOIUrl":"10.1016/j.jco.2024.101904","url":null,"abstract":"","PeriodicalId":50227,"journal":{"name":"Journal of Complexity","volume":"86 ","pages":"Article 101904"},"PeriodicalIF":1.8,"publicationDate":"2024-11-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142586491","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-11-05DOI: 10.1016/j.jco.2024.101907
Harmandeep Singh , Janak Raj Sharma
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.
{"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":"10.1016/j.jco.2024.101907","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":1.8,"publicationDate":"2024-11-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142656796","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-10-31DOI: 10.1016/j.jco.2024.101906
Marcel Fernández , John Livieratos , Sebastià Martín
This paper presents an algorithmic approach to the construction of separating codes. In the first part of the work, the Lovász Local Lemma is used to obtain a lower bound on the code rate. This lower bound matches the previously best-known lower bound. In the second part, it is shown how the technique used in proving the lower bound leads to an algorithm that outputs an instance of a separating code. Moreover, the implications of the algorithm regarding computational complexity are considered. The discussion ends by presenting explicit separating codes with polynomial computational complexity in the length of the code, with rate that improves previously known constructions.
本文提出了一种构建分离码的算法方法。在工作的第一部分，利用 Lovász Local Lemma 获得了码率下限。该下限与之前最著名的下限相吻合。第二部分展示了证明下限时使用的技术如何导致一种算法输出分离代码实例。此外，还考虑了该算法对计算复杂性的影响。讨论的最后，提出了计算复杂度与代码长度成多项式关系的显式分离代码，其速率改进了之前已知的构造。
{"title":"Combinatorial constructions of separating codes","authors":"Marcel Fernández , John Livieratos , Sebastià Martín","doi":"10.1016/j.jco.2024.101906","DOIUrl":"10.1016/j.jco.2024.101906","url":null,"abstract":"<div><div>This paper presents an algorithmic approach to the construction of separating codes. In the first part of the work, the Lovász Local Lemma is used to obtain a lower bound on the code rate. This lower bound matches the previously best-known lower bound. In the second part, it is shown how the technique used in proving the lower bound leads to an algorithm that outputs an instance of a separating code. Moreover, the implications of the algorithm regarding computational complexity are considered. The discussion ends by presenting explicit separating codes with polynomial computational complexity in the length of the code, with rate that improves previously known constructions.</div></div>","PeriodicalId":50227,"journal":{"name":"Journal of Complexity","volume":"86 ","pages":"Article 101906"},"PeriodicalIF":1.8,"publicationDate":"2024-10-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142656797","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-10-22DOI: 10.1016/j.jco.2024.101902
Erich Novak, Kateryna Pozharska, Mathias Sonnleitner, Michaela Szölgyenyi, Henryk Woźniakowski
{"title":"Matthieu Dolbeault is the winner of the 2024 Joseph F. Traub Information-Based Complexity Young Researcher Award","authors":"Erich Novak, Kateryna Pozharska, Mathias Sonnleitner, Michaela Szölgyenyi, Henryk Woźniakowski","doi":"10.1016/j.jco.2024.101902","DOIUrl":"10.1016/j.jco.2024.101902","url":null,"abstract":"","PeriodicalId":50227,"journal":{"name":"Journal of Complexity","volume":"86 ","pages":"Article 101902"},"PeriodicalIF":1.8,"publicationDate":"2024-10-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142525769","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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