{"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}
{"title":"A new subspace iteration algorithm for solving generalized eigenvalue problems in vibration analysis","authors":"Biyi Wang , Hengbin An , Hehu Xie , Zeyao Mo","doi":"10.1016/j.cam.2025.116622","DOIUrl":"10.1016/j.cam.2025.116622","url":null,"abstract":"<div><div>Large scale generalized eigenvalue problems (GEP) arise in many applications, such as the vibration analysis, quantum mechanics, electronic structure calculation. A class of subspace iteration method, the generalized Chebyshev–Davidson (gCD) algorithm, was recently proposed to solve GEP. In the gCD algorithm, the Chebyshev polynomial filter technique is incorporated in the subspace iteration. One of the advantages of the gCD algorithm is that it only concerns matrix vector product, making it suitable for solving large-scale problems. In this paper, based on gCD algorithm, a new subspace iteration algorithm is constructed. In the proposed algorithm, we combine the Chebyshev filter and inexact Rayleigh quotient iteration techniques to enlarge the subspace in the iteration, and the obtained algorithm is named as Chebyshev-RQI subspace (CRS) method. Numerical results for both two dimensional and three dimensional vibration analysis problems show that CRS algorithm is more effective than gCD algorithm measured by iteration numbers and computing time. Specifically, when these two methods are used to compute the smallest 20 eigenpairs of the tested vibration models, CRS converges at least 3.9 times faster than gCD measured by number of iteration and up to 2.5 times faster than gCD measured by solution time. Furthermore, CRS algorithm is more robust than gCD because in some cases, gCD cannot converge while CRS always converges for all test cases.</div></div>","PeriodicalId":50226,"journal":{"name":"Journal of Computational and Applied Mathematics","volume":"468 ","pages":"Article 116622"},"PeriodicalIF":2.1,"publicationDate":"2025-03-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143643365","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":"Polynomial homotopy methods for the equally spaced sparse interpolation problem with jump","authors":"Panpan Zhao , Bo Yu , Libin Jiao","doi":"10.1016/j.cam.2025.116623","DOIUrl":"10.1016/j.cam.2025.116623","url":null,"abstract":"<div><div>In this paper, the equally spaced sparse interpolation problem with jump is considered. Such a problem concerns solving a polynomial system which is a generalization of that in the case without jump. Properties of this polynomial system are investigated for some interesting cases. For some special cases, the numbers of isolated solutions for generic data are accurately estimated; for some other cases, a conjecture on the numbers of solutions is proposed. And then, based on the coefficient parameter homotopy method, a class of efficient algorithms, in which only a few number of paths need to be traced, are proposed. Preliminary numerical tests show that the proposed algorithms are promising.</div></div>","PeriodicalId":50226,"journal":{"name":"Journal of Computational and Applied Mathematics","volume":"468 ","pages":"Article 116623"},"PeriodicalIF":2.1,"publicationDate":"2025-03-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143637513","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":"Global accelerated Hermitian and skew–Hermitian splitting preconditioner for the solution of discrete Stokes problems","authors":"A. Badahmane , A. Ratnani , H. Sadok","doi":"10.1016/j.cam.2025.116620","DOIUrl":"10.1016/j.cam.2025.116620","url":null,"abstract":"<div><div>In fluid mechanics, numerous applications necessitate solving a sequence of linear systems. These systems typically arise from discretizing the Stokes equations using mixed-finite element methods. The matrices that result from this process often exhibit a saddle point structure, which makes the iterative solution of preconditioned linear systems challenging. To effectively solve the large scale and ill-conditioned linear systems, it is necessary to implement efficient linear solvers. We present a global approach, specifically the preconditioned global conjugate gradient (PGCG), aimed at enhancing the performance of preconditioned Hermitian and skew–Hermitian splitting preconditioner <span><math><mrow><mo>(</mo><msub><mrow><mi>P</mi></mrow><mrow><mi>P</mi><mi>H</mi><mi>S</mi><mi>S</mi></mrow></msub><mo>)</mo></mrow></math></span> and accelerated Hermitian and skew–Hermitian splitting preconditioner <span><math><mrow><mo>(</mo><msub><mrow><mi>P</mi></mrow><mrow><mi>A</mi><mi>H</mi><mi>S</mi><mi>S</mi></mrow></msub><mo>)</mo></mrow></math></span>. The new preconditioners can be utilized to expedite the convergence of the generalized minimal residual (GMRES) method. We evaluate the effectiveness of the preconditioned iterative methods by considering the Central Processing Unit (<span><math><mi>CPU</mi></math></span>) times and numbers of the <span><math><mi>P</mi></math></span>GMRES iterations. The numerical results indicate that incorporating <span><math><mi>P</mi></math></span>GCG method improves the performance of the preconditioners <span><math><msub><mrow><mi>P</mi></mrow><mrow><mi>P</mi><mi>H</mi><mi>S</mi><mi>S</mi></mrow></msub></math></span> and <span><math><msub><mrow><mi>P</mi></mrow><mrow><mi>A</mi><mi>H</mi><mi>S</mi><mi>S</mi></mrow></msub></math></span>.</div></div>","PeriodicalId":50226,"journal":{"name":"Journal of Computational and Applied Mathematics","volume":"467 ","pages":"Article 116620"},"PeriodicalIF":2.1,"publicationDate":"2025-03-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143601663","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":"Greedy Kaczmarz methods for nonlinear equation","authors":"Li Liu, Wei-Guo Li, Wen-Di Bao, Li-Li Xing","doi":"10.1016/j.cam.2025.116630","DOIUrl":"10.1016/j.cam.2025.116630","url":null,"abstract":"<div><div>A class of randomized Kaczmarz methods for solving nonlinear systems of equations was introduced by Q. Wang and W. Li. These methods significantly reduce computational and storage requirements by computing only a single row of the Jacobian matrix in each iteration, rather than the entire matrix. Building upon this approach and the greedy randomized Kaczmarz method for linear systems, we propose two novel methods for solving overdetermined or singular nonlinear systems: the nonlinear greedy deterministic Kaczmarz (NGDK) method and the nonlinear greedy randomized Kaczmarz (NGRK) method. This paper presents the local convergence analysis and numerical experiments for the proposed methods. The experimental results demonstrate the efficacy of these methods in the case of noise-free data.</div></div>","PeriodicalId":50226,"journal":{"name":"Journal of Computational and Applied Mathematics","volume":"467 ","pages":"Article 116630"},"PeriodicalIF":2.1,"publicationDate":"2025-03-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143601661","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}