{"title":"An improved theoretical analysis of convolutional sparse coding using stripe coherence","authors":"Haifeng Li , 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}
{"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}
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 , Paulo Henrique Lopes Silva , João Paulo Caraú de Oliveira , Raimundo Leandro Andrade Marques , 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}
Xuejing Zhang , Huanhuan Ma , Xinyu Wu , Jiansong Deng
{"title":"A boundary-precise method of numerical integration over implicitly defined regions","authors":"Xuejing Zhang , Huanhuan Ma , Xinyu Wu , 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}
{"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}
{"title":"Conditional correlation estimation and serial dependence identification","authors":"Kewin Pączek , Damian Jelito , Marcin Pitera , 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}
{"title":"Existence theorems of generalized K-lateral support equilibria via local cooperative strategies for multi-player pure strategy games in tensor form","authors":"Chenli Xu , Kaixin Gao , Zheng-Hai Huang","doi":"10.1016/j.cam.2025.116634","DOIUrl":"10.1016/j.cam.2025.116634","url":null,"abstract":"<div><div>In this paper, we introduce a novel equilibrium framework in pure strategy games called <span><math><mi>K</mi></math></span>-lateral support equilibrium (<span><math><mi>K</mi></math></span>-LSE), encompassing unilateral support equilibrium and Berge equilibrium as special cases. This framework applies to a broad class of <span><math><mi>n</mi></math></span>-person pure strategy games, with the values of <span><math><mi>K</mi></math></span> varying from 1 to <span><math><mrow><mi>n</mi><mo>−</mo><mn>1</mn></mrow></math></span>. Two fundamental theorems provide necessary and sufficient conditions for the existence of strategy profiles corresponding to pure <span><math><mi>K</mi></math></span>-LSEs. When the strategy set of each player has finite elements, we develop a tensor representation of <span><math><mi>K</mi></math></span>-LSEs and design an algorithm for computing <span><math><mi>K</mi></math></span>-LSEs in <span><math><mi>n</mi></math></span>-player pure strategy games. This algorithm provides a useful method with tensor representation for addressing equilibrium problems in complex high-dimensional game scenarios. The effectiveness of this algorithm is demonstrated through numerical examples involving a four-player game, where the algorithm successfully identifies all unilateral, bilateral and Berge equilibria. Additionally, the relationships of different <span><math><mi>K</mi></math></span>-LSEs are also established and discussed.</div></div>","PeriodicalId":50226,"journal":{"name":"Journal of Computational and Applied Mathematics","volume":"468 ","pages":"Article 116634"},"PeriodicalIF":2.1,"publicationDate":"2025-03-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143643367","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}
Guanglei Sun , Youlin Shang , Xiaoqiang Wang , Roxin Zhang , Deqiang Qu
{"title":"An efficient algorithm via a novel one-parameter filled function based on general univariate functions for unconstrained global optimization","authors":"Guanglei Sun , Youlin Shang , Xiaoqiang Wang , Roxin Zhang , Deqiang Qu","doi":"10.1016/j.cam.2025.116632","DOIUrl":"10.1016/j.cam.2025.116632","url":null,"abstract":"<div><div>The global optimization algorithm based on filled function is considered to be effective for solving global optimization problems, attracting significant attention from scholars due to its strong ability to escape from local minimizers. The performance of this algorithm is directly affected by the properties of the filled function adopted. To improve computational efficiency, a new general form of filled function proposed one-parameter is provided in this paper, which is constructed from the general forms of two unary functions with monotonic properties. Theoretical results demonstrate that the newly-defined function satisfies the definition of filled function, and exhibits better mathematical properties. Based on these properties, a novel filled function algorithm for unconstrained global optimization problems is given. The advantage of this algorithm is that it only needs to minimize the filled function instead of alternately minimizing the objective function and the filled function, which theoretically reduces the number of iterations, and to search the optimal solution of the filled function in the whole search space rather than the neighbourhood of the current local optimal solution, which reduces the search blind spots. The comparison results show that our algorithm has dominant superiority in computational speed and accuracy as well as stability.</div></div>","PeriodicalId":50226,"journal":{"name":"Journal of Computational and Applied Mathematics","volume":"468 ","pages":"Article 116632"},"PeriodicalIF":2.1,"publicationDate":"2025-03-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143643366","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}
Xi’an Li , Jinran Wu , Yujia Huang , Zhe Ding , Xin Tai , Liang Liu , You-Gan Wang
{"title":"Fourier-feature induced physics informed randomized neural network method to solve the biharmonic equation","authors":"Xi’an Li , Jinran Wu , Yujia Huang , Zhe Ding , Xin Tai , Liang Liu , You-Gan Wang","doi":"10.1016/j.cam.2025.116635","DOIUrl":"10.1016/j.cam.2025.116635","url":null,"abstract":"<div><div>To address the sensitivity of parameters and limited precision for randomized neural network method (RNN) with common activation functions, such as sigmoid, tangent, and Gaussian, in solving high-order partial differential equations (PDEs) relevant to scientific computation and engineering applications, this work develops a Fourier-feature induced physics informed single layer RNN (FPISRNN) method. This approach aims to approximate the solution for a class of fourth-order biharmonic equation with two boundary conditions on both unitized and non-unitized domains. By carefully calculating the differential and boundary operators of the biharmonic equation on discretized collections, the solution for this high-order equation is reformulated as a linear least squares minimization problem. We further evaluate the FPISRNN method with varying hidden nodes and scaling factors for uniform distribution initialization, and then determine the optimal range for these two hyperparameters. Numerical experiments and comparative analyses demonstrate that the proposed FPISRNN method is more stable, robust, precise, and efficient than other FPISRNN approaches in solving biharmonic equations for both regular and irregular domains.</div></div>","PeriodicalId":50226,"journal":{"name":"Journal of Computational and Applied Mathematics","volume":"468 ","pages":"Article 116635"},"PeriodicalIF":2.1,"publicationDate":"2025-03-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143637512","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}
{"title":"Optimal conditions and duality results for a semi-infinite variational programming problem and its Mond–Weir dual involving Caputo–Fabrizio fractional derivatives","authors":"Anurag Jayswal, Gaurav Uniyal","doi":"10.1016/j.cam.2025.116628","DOIUrl":"10.1016/j.cam.2025.116628","url":null,"abstract":"<div><div>In this paper, we deal with a Semi-infinite variational programming (SIVP) problem involving Caputo–Fabrizio (CF) fractional derivative operator. By using Slater’s constraint qualification (SCQ) and some generalized convexity assumptions, we first establish KKT necessary and sufficient optimality conditions for SIVP problem. Later, we study the Mond–Weir type dual model and discuss several duality theorems. Additionally, some numerical examples have been given to support theoretical results.</div></div>","PeriodicalId":50226,"journal":{"name":"Journal of Computational and Applied Mathematics","volume":"468 ","pages":"Article 116628"},"PeriodicalIF":2.1,"publicationDate":"2025-03-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143637514","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}