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Recovery conditions for generalized orthogonal matching pursuit based coherence
IF 2.1 2区 数学
Journal of Computational and Applied Mathematics Pub Date : 2025-03-27 DOI: 10.1016/j.cam.2025.116648
Hanbing Liu , Chongjun Li , Yijun Zhong
{"title":"Recovery conditions for generalized orthogonal matching pursuit based coherence","authors":"Hanbing Liu ,&nbsp;Chongjun Li ,&nbsp;Yijun Zhong","doi":"10.1016/j.cam.2025.116648","DOIUrl":"10.1016/j.cam.2025.116648","url":null,"abstract":"<div><div>In sparse approximation, a key theoretical issue is the guarantee conditions for the exact recovery of <span><math><mi>s</mi></math></span>-sparse signals. The Orthogonal Matching Pursuit (OMP) and the Generalized Orthogonal Matching Pursuit (GOMP) are two important algorithms commonly used in sparse approximation. The main difference is that the OMP algorithm selects one atom in each iteration, while the GOMP algorithm selects multiple atoms. In the current theoretical analysis, the GOMP algorithm can only guarantee the selection of at least one correct atom in each iteration. However, in practical applications, the GOMP algorithm has been shown to select multiple correct atoms in each iteration but lacks theoretical guarantee conditions. In this paper, we discuss the extended coherence-based conditions for exact support recovery of the <span><math><mi>s</mi></math></span>-sparse signals using the GOMP algorithm. We propose several sufficient conditions for the GOMP algorithm to select <span><math><mi>M</mi></math></span> (<span><math><mrow><mn>1</mn><mo>≤</mo><mi>M</mi><mo>≤</mo><mi>s</mi></mrow></math></span>) correct atoms in each iteration in noiseless and bounded-noise cases respectively. Some of the conditions involve the decay of nonzero entries in sparse signals. Numerical experiments demonstrate the effectiveness of the proposed sufficient conditions.</div></div>","PeriodicalId":50226,"journal":{"name":"Journal of Computational and Applied Mathematics","volume":"469 ","pages":"Article 116648"},"PeriodicalIF":2.1,"publicationDate":"2025-03-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143734733","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}
引用次数: 0
Effectiveness of Picard–Abbas iteration for fixed point approximation of mappings satisfying condition (E)
IF 2.1 2区 数学
Journal of Computational and Applied Mathematics Pub Date : 2025-03-26 DOI: 10.1016/j.cam.2025.116649
Bashir Nawaz , Krzysztof Gdawiec , Kifayat Ullah
{"title":"Effectiveness of Picard–Abbas iteration for fixed point approximation of mappings satisfying condition (E)","authors":"Bashir Nawaz ,&nbsp;Krzysztof Gdawiec ,&nbsp;Kifayat Ullah","doi":"10.1016/j.cam.2025.116649","DOIUrl":"10.1016/j.cam.2025.116649","url":null,"abstract":"<div><div>In this paper, we investigate the convergence properties of mappings that satisfy condition (<span><math><mi>E</mi></math></span>) by employing the recently introduced Picard–Abbas iteration process. We establish both weak and strong fixed-point convergence results for these mappings. To validate our findings, we provide a novel numerical example. Furthermore, we generate polynomiographs using the proposed iteration process and compare them with those obtained from other methods. This comparison highlights the effectiveness and potential advantages of our approach.</div></div>","PeriodicalId":50226,"journal":{"name":"Journal of Computational and Applied Mathematics","volume":"469 ","pages":"Article 116649"},"PeriodicalIF":2.1,"publicationDate":"2025-03-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143739210","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}
引用次数: 0
A generalized Legendre transform method and its applications
IF 2.1 2区 数学
Journal of Computational and Applied Mathematics Pub Date : 2025-03-25 DOI: 10.1016/j.cam.2025.116646
Imtiaz Waheed, Mujeeb ur Rehman
{"title":"A generalized Legendre transform method and its applications","authors":"Imtiaz Waheed,&nbsp;Mujeeb ur Rehman","doi":"10.1016/j.cam.2025.116646","DOIUrl":"10.1016/j.cam.2025.116646","url":null,"abstract":"<div><div>The article aims to develop the shifted Legendre transform method in the context of <span><math><mi>Ψ</mi></math></span>-fractional calculus, termed as the <span><math><mi>Ψ</mi></math></span>-shifted Legendre transform. The proposed transform method generalizes the classical Legendre transform. The <span><math><mi>Ψ</mi></math></span>-shifted Legendre transform is applied to differential and integral operators. Moreover, the inverse operator, various operational properties of <span><math><mi>Ψ</mi></math></span>-shifted Legendre polynomials, and the <span><math><mi>Ψ</mi></math></span>-shifted transform method are investigated. The convolution for the <span><math><mi>Ψ</mi></math></span>-shifted Legendre transform in the framework of <span><math><mi>Ψ</mi></math></span>-fractional calculus is also determined. Finally, fractional differential equations involving the <span><math><mi>Ψ</mi></math></span>-fractional derivative are solved using the <span><math><mi>Ψ</mi></math></span>-shifted Legendre transform method.</div></div>","PeriodicalId":50226,"journal":{"name":"Journal of Computational and Applied Mathematics","volume":"468 ","pages":"Article 116646"},"PeriodicalIF":2.1,"publicationDate":"2025-03-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143706103","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}
引用次数: 0
Unveiling fractional-order dynamics: A new method for analyzing Rössler Chaos
IF 2.1 2区 数学
Journal of Computational and Applied Mathematics Pub Date : 2025-03-24 DOI: 10.1016/j.cam.2025.116639
Mudasir Younis , Haroon Ahmad , Mahpeyker Ozturk , Fahim Ud Din , Muhammad Qasim
{"title":"Unveiling fractional-order dynamics: A new method for analyzing Rössler Chaos","authors":"Mudasir Younis ,&nbsp;Haroon Ahmad ,&nbsp;Mahpeyker Ozturk ,&nbsp;Fahim Ud Din ,&nbsp;Muhammad Qasim","doi":"10.1016/j.cam.2025.116639","DOIUrl":"10.1016/j.cam.2025.116639","url":null,"abstract":"<div><div>In this manuscript, we investigate the fractional-order Rössler attractor using the Atangana–Baleanu derivative within the metric fixed point theory framework. We establish the existence and uniqueness criteria for the fractional-order Rössler model by employing the <span><math><mi>ℱ</mi></math></span>-type rational contraction technique through the lens of Atangana–Baleanu in the environment of extended suprametric space. Furthermore, we construct a solid mathematical foundation by applying interpolative Kannan and Reich-Rus-Ćirić type contractions together with specific examples to validate the fixed point results. The two-step Lagrange method performs fractional derivative approximation to study the attractor’s geometric evolution under different parametric conditions. Numerical simulations created new classifications of chaotic behavior that enhance our understanding of fractional dynamics working with chaos theory.</div></div>","PeriodicalId":50226,"journal":{"name":"Journal of Computational and Applied Mathematics","volume":"468 ","pages":"Article 116639"},"PeriodicalIF":2.1,"publicationDate":"2025-03-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143706104","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}
引用次数: 0
An improved theoretical analysis of convolutional sparse coding using stripe coherence
IF 2.1 2区 数学
Journal of Computational and Applied Mathematics Pub Date : 2025-03-24 DOI: 10.1016/j.cam.2025.116631
Haifeng Li , Wengu Chen
{"title":"An improved theoretical analysis of convolutional sparse coding using stripe coherence","authors":"Haifeng Li ,&nbsp;Wengu Chen","doi":"10.1016/j.cam.2025.116631","DOIUrl":"10.1016/j.cam.2025.116631","url":null,"abstract":"<div><div>Convolutional sparse coding has proven to be very effective in a wide range of applications. Recent work addressed the theoretical performance of global orthogonal matching pursuit (OMP) using the stripe coherence that is a stronger characterization of the convolutional dictionary. In this paper, we further provide the theoretical analysis of convolutional sparse model. Our result improves the guarantee condition for global OMP based on convolutional sparse model. We also provide the theoretical guarantee for basis pursuit using stripe coherence based on convolutional sparse model, which is absent in the existing results.</div></div>","PeriodicalId":50226,"journal":{"name":"Journal of Computational and Applied Mathematics","volume":"469 ","pages":"Article 116631"},"PeriodicalIF":2.1,"publicationDate":"2025-03-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143714441","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}
引用次数: 0
An improved PRP conjugate gradient algorithm with a damping factor within an automatic restarting strategy
IF 2.1 2区 数学
Journal of Computational and Applied Mathematics Pub Date : 2025-03-22 DOI: 10.1016/j.cam.2025.116638
Xiao Liang Dong
{"title":"An improved PRP conjugate gradient algorithm with a damping factor within an automatic restarting strategy","authors":"Xiao Liang Dong","doi":"10.1016/j.cam.2025.116638","DOIUrl":"10.1016/j.cam.2025.116638","url":null,"abstract":"<div><div>In this paper, we present an improved Polak–Ribière–Polyak (PRP) conjugate gradient algorithm, in which the search direction satisfies the sufficient descent condition with strong Wolfe conditions. A “circuit breaker” mechanism is suggested in the monitoring and pre-warning system concerned with a poor approximation to the scalar β<span><math><msubsup><mrow></mrow><mrow><mi>k</mi></mrow><mrow><mi>P</mi><mi>R</mi><mi>P</mi></mrow></msubsup></math></span>. The resulting instinct self-correcting property is satisfied at each iteration, which can be viewed as the inheritance and development of the original PRP method. Meanwhile, several auxiliary functions are introduced, which achieve twin goals of manipulating the magnitude of conjugate gradient parameter and making swift changes to incorrect predictions if jamming occurs in actual computation. Under mild conditions, we establish the global convergence of the new algorithms and its variants for the general function. Numerical results show our algorithms are practical and effective for the test problems. Finally, the preliminary numerical experiments are given to indicate the efficiency of the proposed methods for image restoration.</div></div>","PeriodicalId":50226,"journal":{"name":"Journal of Computational and Applied Mathematics","volume":"468 ","pages":"Article 116638"},"PeriodicalIF":2.1,"publicationDate":"2025-03-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143706102","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}
引用次数: 0
A Parallel Iterative hybrid Gauss–Jacobi–Seidel method
IF 2.1 2区 数学
Journal of Computational and Applied Mathematics Pub Date : 2025-03-22 DOI: 10.1016/j.cam.2025.116629
Matheus da Silva Menezes , Paulo Henrique Lopes Silva , João Paulo Caraú de Oliveira , Raimundo Leandro Andrade Marques , Ivan Mezzomo
{"title":"A Parallel Iterative hybrid Gauss–Jacobi–Seidel method","authors":"Matheus da Silva Menezes ,&nbsp;Paulo Henrique Lopes Silva ,&nbsp;João Paulo Caraú de Oliveira ,&nbsp;Raimundo Leandro Andrade Marques ,&nbsp;Ivan Mezzomo","doi":"10.1016/j.cam.2025.116629","DOIUrl":"10.1016/j.cam.2025.116629","url":null,"abstract":"<div><div>In this paper, we introduce a new iterative hybrid method to find the solution of linear algebraic systems based on the Gauss–Jacobi and Gauss–Seidel methods, named Jacobi–Seidel Parallel Iterative Method, JASPIoM for short. This method shows a iteration matrix that allows to parallelize the processing and can be utilized in serial or parallel architectures. The mathematical formulation is presented and the tests are performed in parallel ambiance and its performance is evaluated, considering the time of execution, in comparison to the serial and parallelized Gauss–Jacobi method and serial Gauss–Seidel method. The computational experiment aimed at focusing on the differences in performance, considering the speedup of execution in serial and parallel context. The results show that the JASPIoM method presents good performance, indicating the efficiency and potential of this scheme.</div></div>","PeriodicalId":50226,"journal":{"name":"Journal of Computational and Applied Mathematics","volume":"468 ","pages":"Article 116629"},"PeriodicalIF":2.1,"publicationDate":"2025-03-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143697720","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}
引用次数: 0
A boundary-precise method of numerical integration over implicitly defined regions
IF 2.1 2区 数学
Journal of Computational and Applied Mathematics Pub Date : 2025-03-21 DOI: 10.1016/j.cam.2025.116637
Xuejing Zhang , Huanhuan Ma , Xinyu Wu , Jiansong Deng
{"title":"A boundary-precise method of numerical integration over implicitly defined regions","authors":"Xuejing Zhang ,&nbsp;Huanhuan Ma ,&nbsp;Xinyu Wu ,&nbsp;Jiansong Deng","doi":"10.1016/j.cam.2025.116637","DOIUrl":"10.1016/j.cam.2025.116637","url":null,"abstract":"<div><div>In this paper, we introduce a boundary-precise method of numerical integration over implicitly defined regions using the idea of isogeometry. This method ensures precise boundary representations during the integration process by establishing proper local parameterizations near these boundaries based on the implicit representations. We establish an adaptive algorithm for the method, and provide two examples for integration over different types of regions. We also calculate the error while integrating by this method and provide detailed error estimates. When solving partial differential equations (PDEs) using weighted extended B-spline (WEB) method, the augmented matrix in the linear system of Galerkin framework is derived through integration, where this boundary-precise method can be applied. Three different types of examples are displayed and the results demonstrate the convergence of error and the stability of order.</div></div>","PeriodicalId":50226,"journal":{"name":"Journal of Computational and Applied Mathematics","volume":"468 ","pages":"Article 116637"},"PeriodicalIF":2.1,"publicationDate":"2025-03-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143686619","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}
引用次数: 0
Closed-form solution-based fuzzy utility vectors acquired from trapezoidal fuzzy pairwise comparison matrices using logarithmic quadratic programming for improving fuzzy AHP decision-making systems
IF 2.1 2区 数学
Journal of Computational and Applied Mathematics Pub Date : 2025-03-18 DOI: 10.1016/j.cam.2025.116647
Zhou-Jing Wang
{"title":"Closed-form solution-based fuzzy utility vectors acquired from trapezoidal fuzzy pairwise comparison matrices using logarithmic quadratic programming for improving fuzzy AHP decision-making systems","authors":"Zhou-Jing Wang","doi":"10.1016/j.cam.2025.116647","DOIUrl":"10.1016/j.cam.2025.116647","url":null,"abstract":"<div><div>Closed-form solution-based fuzzy utility vectors acquired from trapezoidal fuzzy pairwise comparison matrices (TFPCMs) play significant roles in examining the quality of fuzzy evaluations in TFPCMs and improving the efficiency of fuzzy analytic hierarchy process based decision-making systems. This paper introduces a concept of consistent TFPCMs and develops crucial properties to expose inherent constraints among increasing spread indices, decreasing spread indices, and core and support uncertainty indices of fuzzy evaluations in a consistent TFPCM. The paper proposes two normalization frames called core normalized trapezoidal fuzzy vectors and support normalized trapezoidal fuzzy vectors. By categorizing all TFPCMs with the same order into two groups, two logarithmic quadratic programming models are respectively built to seek normalized trapezoidal fuzzy utility vectors from TFPCMs. The two logarithmic quadratic programming models are subsequently integrated into one whose closed-form solution is identified by Lagrange multiplier method. A closed-form solution-based consistency index is presented to figure out inconsistency degrees of TFPCMs. An illustration with one consistent TFPCM and five inconsistent TFPCMs is offered to reveal the use of the presented method and a study comparing the developed model with fuzzy mean methods and fuzzy eigenvector methods is conducted to demonstrate the performance and superiority of the closed-form solution-based fuzzy utility acquisition method.</div></div>","PeriodicalId":50226,"journal":{"name":"Journal of Computational and Applied Mathematics","volume":"468 ","pages":"Article 116647"},"PeriodicalIF":2.1,"publicationDate":"2025-03-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143697719","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}
引用次数: 0
Conditional correlation estimation and serial dependence identification
IF 2.1 2区 数学
Journal of Computational and Applied Mathematics Pub Date : 2025-03-18 DOI: 10.1016/j.cam.2025.116633
Kewin Pączek , Damian Jelito , Marcin Pitera , Agnieszka Wyłomańska
{"title":"Conditional correlation estimation and serial dependence identification","authors":"Kewin Pączek ,&nbsp;Damian Jelito ,&nbsp;Marcin Pitera ,&nbsp;Agnieszka Wyłomańska","doi":"10.1016/j.cam.2025.116633","DOIUrl":"10.1016/j.cam.2025.116633","url":null,"abstract":"<div><div>It has been recently shown in Jaworski et al. (2024), ‘A note on the equivalence between the conditional uncorrelation and the independence of random variables’, Electronic Journal of Statistics 18(1), that one can characterize the independence of random variables via the family of conditional correlations on quantile-induced sets. This effectively shows that the localized linear measure of dependence is able to detect any form of nonlinear dependence for appropriately chosen conditioning sets. In this paper, we expand this concept, focusing on the statistical properties of conditional correlation estimators and their potential usage in serial dependence identification. In particular, we show how to estimate conditional correlations in generic and serial dependence setups, discuss key properties of the related estimators, define the conditional equivalent of the autocorrelation function, and provide a series of examples which prove that the proposed framework could be efficiently used in many practical econometric applications.</div></div>","PeriodicalId":50226,"journal":{"name":"Journal of Computational and Applied Mathematics","volume":"468 ","pages":"Article 116633"},"PeriodicalIF":2.1,"publicationDate":"2025-03-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143686620","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}
引用次数: 0
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