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Two inertial-relaxed hybridized CG projection-based algorithms for solving nonlinear monotone equations applied in image restoration
IF 2.1 2区 数学
Journal of Computational and Applied Mathematics Pub Date : 2025-02-06 DOI: 10.1016/j.cam.2025.116546
Xuejie Ma , Sixing Yang , Pengjie Liu
{"title":"Two inertial-relaxed hybridized CG projection-based algorithms for solving nonlinear monotone equations applied in image restoration","authors":"Xuejie Ma ,&nbsp;Sixing Yang ,&nbsp;Pengjie Liu","doi":"10.1016/j.cam.2025.116546","DOIUrl":"10.1016/j.cam.2025.116546","url":null,"abstract":"<div><div>In this paper, we introduce two inertial-relaxed hybridized conjugate gradient projection-based algorithms for solving nonlinear monotone equations. Compared to traditional inertial-relaxed algorithms for solving such nonlinear equations, our algorithms utilize three-step iterative information to generate inertial iterates. The search directions of two proposed algorithms each include a flexible non-zero vector and feature their own self-adaptive hybrid structure to enhance their adaptability. Both search directions satisfy the sufficient descent and trust region properties, eliminating the need for additional conditions. In the theoretical analysis of global convergence and convergence rate results, both proposed algorithms exhibit similarities. We begin by using the first proposed algorithm to establish the global convergence without requiring the Lipschitz continuity assumption. Furthermore, under additional assumptions, we demonstrate the convergence rate of this algorithm. To evaluate their effectiveness, we conduct comparative tests against existing algorithms using nonlinear equations. Moreover, the practicality of the two proposed algorithms is shown through applications on image restoration problems.</div></div>","PeriodicalId":50226,"journal":{"name":"Journal of Computational and Applied Mathematics","volume":"464 ","pages":"Article 116546"},"PeriodicalIF":2.1,"publicationDate":"2025-02-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143376709","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
Construction of quasi-localized dual bases in reproducing kernel Hilbert spaces
IF 2.1 2区 数学
Journal of Computational and Applied Mathematics Pub Date : 2025-02-05 DOI: 10.1016/j.cam.2025.116545
Helmut Harbrecht , Rüdiger Kempf , Michael Multerer
{"title":"Construction of quasi-localized dual bases in reproducing kernel Hilbert spaces","authors":"Helmut Harbrecht ,&nbsp;Rüdiger Kempf ,&nbsp;Michael Multerer","doi":"10.1016/j.cam.2025.116545","DOIUrl":"10.1016/j.cam.2025.116545","url":null,"abstract":"<div><div>A straightforward way to represent the kernel approximant of a function, known by a finite set of samples, within a reproducing kernel Hilbert space is through the canonical dual pair. The canonical dual pair consists of the basis of kernel translates and the corresponding Lagrange basis. From a numerical perspective, one is particularly interested in dual pairs such that the dual basis is <em>quasi-local</em> meaning that it can be well approximated using only a small subset of the data sites. This implies that the inverse Gramian is approximately sparse. In this case, the kernel approximant is efficiently computable by multiplying a sparse matrix with the data vector. We present two methods for finding such quasi-localized dual bases. First, we adapt the idea of localizing the Lagrange basis, which yields an approximate canonical dual pair and extend this idea to derive a new, symmetric preconditioner for kernel matrices. Second, we use samplets to obtain multiresolution versions of dual bases. Samplets are localized discrete signed measures constructed such that their respective measure integrals of polynomials up to a certain degree vanish. Therefore, the kernel matrix and its inverse are compressible to sparse matrices in samplet coordinates for asymptotically smooth kernels. We provide benchmark experiments in two spatial dimensions to demonstrate the compression power of both approaches and apply the new preconditioner to implicit surface reconstruction in computer graphics.</div></div>","PeriodicalId":50226,"journal":{"name":"Journal of Computational and Applied Mathematics","volume":"465 ","pages":"Article 116545"},"PeriodicalIF":2.1,"publicationDate":"2025-02-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143436843","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}
引用次数: 0
Dynamic complexity of fifth-dimensional Henon map with Lyapunov exponent, permutation entropy, bifurcation patterns and chaos
IF 2.1 2区 数学
Journal of Computational and Applied Mathematics Pub Date : 2025-02-01 DOI: 10.1016/j.cam.2025.116547
Md. Asraful Islam, Ivna Ratul Hassan, Payer Ahmed
{"title":"Dynamic complexity of fifth-dimensional Henon map with Lyapunov exponent, permutation entropy, bifurcation patterns and chaos","authors":"Md. Asraful Islam,&nbsp;Ivna Ratul Hassan,&nbsp;Payer Ahmed","doi":"10.1016/j.cam.2025.116547","DOIUrl":"10.1016/j.cam.2025.116547","url":null,"abstract":"<div><div>The research analyses how the classic Henon map's adjustments affected the system's dynamical behavior and bifurcation frameworks. Analyzing the updated Henon map's parameter space reveals intricate patterns and transitions as the system bifurcates. The dynamical evolution of the map is studied through numerical simulations, providing insights into the emergence of novel features and behaviors. Furthermore, the Lyapunov exponent of the fifth-dimensional Henon map is calculated to quantify the system's sensitivity to initial conditions. The Lyapunov exponent serves as a crucial indicator of chaos and stability, aiding in the characterization of the map's complex dynamics. The paper presents dissipative, permutation entropy, basin of attraction and a comprehensive examination of the Lyapunov exponent across parameter ranges, shedding light on the system's overall stability and chaos. A number of theorems and a study on stability are demonstrated in this article. The results highlight the profound impact of modifications on the Henon map's dynamics, offering a deeper understanding of its behavior and bifurcation scenarios. This research adds to the larger body of knowledge in the areas of unusual systems and how they act in the context of the chaos hypothesis on the behavior of the Henon map. The results show that parameter adjustments substantially shape the dynamical complexity of the Henon map. This study presents a fifth-dimensional Hénon map-based encryption and random bit generator for secure image cryptography.</div></div>","PeriodicalId":50226,"journal":{"name":"Journal of Computational and Applied Mathematics","volume":"466 ","pages":"Article 116547"},"PeriodicalIF":2.1,"publicationDate":"2025-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143551034","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
On sparse grid interpolation for American option pricing with multiple underlying assets
IF 2.1 2区 数学
Journal of Computational and Applied Mathematics Pub Date : 2025-01-31 DOI: 10.1016/j.cam.2025.116544
Jiefei Yang, Guanglian Li
{"title":"On sparse grid interpolation for American option pricing with multiple underlying assets","authors":"Jiefei Yang,&nbsp;Guanglian Li","doi":"10.1016/j.cam.2025.116544","DOIUrl":"10.1016/j.cam.2025.116544","url":null,"abstract":"<div><div>In this work, we develop a novel efficient quadrature and sparse grid based polynomial interpolation method to price American options with multiple underlying assets. The approach is based on first formulating the pricing of American options using dynamic programming, and then employing static sparse grids to interpolate the continuation value function at each time step. To achieve high efficiency, we first transform the domain from <span><math><msup><mrow><mi>R</mi></mrow><mrow><mi>d</mi></mrow></msup></math></span> to <span><math><msup><mrow><mrow><mo>(</mo><mo>−</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>)</mo></mrow></mrow><mrow><mi>d</mi></mrow></msup></math></span> via a scaled tanh map, and then remove the boundary singularity of the resulting multivariate function over <span><math><msup><mrow><mrow><mo>(</mo><mo>−</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>)</mo></mrow></mrow><mrow><mi>d</mi></mrow></msup></math></span> by a bubble function and simultaneously, to significantly reduce the number of interpolation points. We rigorously establish that with a proper choice of the bubble function, the resulting function has bounded mixed derivatives up to a certain order, which provides theoretical underpinnings for the use of sparse grids. Numerical experiments for American arithmetic and geometric basket put options with the number of underlying assets up to 16 are presented to validate the effectiveness of our approach.</div></div>","PeriodicalId":50226,"journal":{"name":"Journal of Computational and Applied Mathematics","volume":"464 ","pages":"Article 116544"},"PeriodicalIF":2.1,"publicationDate":"2025-01-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143289443","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}
引用次数: 0
An improved proximal primal–dual ALM-based algorithm with convex combination proximal centers for equality-constrained convex programming in basis pursuit practical problems
IF 2.1 2区 数学
Journal of Computational and Applied Mathematics Pub Date : 2025-01-30 DOI: 10.1016/j.cam.2025.116531
Xihong Yan , Hao Li , Chuanlong Wang , Danqing Zhou , Junfeng Yang
{"title":"An improved proximal primal–dual ALM-based algorithm with convex combination proximal centers for equality-constrained convex programming in basis pursuit practical problems","authors":"Xihong Yan ,&nbsp;Hao Li ,&nbsp;Chuanlong Wang ,&nbsp;Danqing Zhou ,&nbsp;Junfeng Yang","doi":"10.1016/j.cam.2025.116531","DOIUrl":"10.1016/j.cam.2025.116531","url":null,"abstract":"<div><div>In this paper, we propose a novel proximal point Lagrangian-based method for solving convex programming problems with linear equality constraints, where the proximal centers are constructed using convex combinations of the iterates. The new method preserves all the favorable characteristics of customized proximal point algorithm, including convergence of both the primal and dual iterates, as well as the ability to derive closed-form solutions for subproblems under certain conditions. Furthermore, we prove the global convergence and establish an <span><math><mrow><mi>O</mi><mrow><mo>(</mo><mn>1</mn><mo>/</mo><mi>K</mi><mo>)</mo></mrow></mrow></math></span> ergodic sublinear convergence rate of our algorithm under mild assumptions. Finally, numerical experiments conducted on basis pursuit and equality-constrained quadratic programming problems demonstrate the superior performance of our proposed algorithm.</div></div>","PeriodicalId":50226,"journal":{"name":"Journal of Computational and Applied Mathematics","volume":"464 ","pages":"Article 116531"},"PeriodicalIF":2.1,"publicationDate":"2025-01-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143170292","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 accelerated double-step derivative-free projection method based algorithm using Picard–Mann iterative process for solving convex constrained nonlinear equations
IF 2.1 2区 数学
Journal of Computational and Applied Mathematics Pub Date : 2025-01-30 DOI: 10.1016/j.cam.2025.116541
J.K. Liu, B. Tang, T. Liu, Z.T. Yang, S. Liang
{"title":"An accelerated double-step derivative-free projection method based algorithm using Picard–Mann iterative process for solving convex constrained nonlinear equations","authors":"J.K. Liu,&nbsp;B. Tang,&nbsp;T. Liu,&nbsp;Z.T. Yang,&nbsp;S. Liang","doi":"10.1016/j.cam.2025.116541","DOIUrl":"10.1016/j.cam.2025.116541","url":null,"abstract":"<div><div>In this paper, we propose a double-step derivative-free projection method to solve large-scale nonlinear equations with convex constraints, which is an extension of the popular double direction and double-step method for solving unconstrained optimization problems. Its search direction contains the acceleration parameter and the correction parameter obtained by utilizing the approximate Jacobian matrix and the Picard–Mann hybrid iteration process, respectively. We prove the global convergence of the proposed method under the pseudo-monotone property of the mapping. Moreover, the R-linear convergence rate of the proposed method is presented. Numerical experiments verify the effectiveness of the proposed method.</div></div>","PeriodicalId":50226,"journal":{"name":"Journal of Computational and Applied Mathematics","volume":"464 ","pages":"Article 116541"},"PeriodicalIF":2.1,"publicationDate":"2025-01-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143170294","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
Spatially nonhomogeneous patterns for a modified Leslie–Gower model with predator-taxis
IF 2.1 2区 数学
Journal of Computational and Applied Mathematics Pub Date : 2025-01-30 DOI: 10.1016/j.cam.2025.116542
Caijuan Jia, Yan Meng, Jiaxin Xiao
{"title":"Spatially nonhomogeneous patterns for a modified Leslie–Gower model with predator-taxis","authors":"Caijuan Jia,&nbsp;Yan Meng,&nbsp;Jiaxin Xiao","doi":"10.1016/j.cam.2025.116542","DOIUrl":"10.1016/j.cam.2025.116542","url":null,"abstract":"<div><div>In this paper, we investigate a modified Leslie–Gower predator–prey model with predator-taxis under the Neumann boundary condition. Firstly, the boundness of solution and the global stability conditions of the positive equilibrium are performed. Secondly, we take predator-taxis sensitivity coefficient as a potential bifurcation parameter for Turing bifurcation and analyze multiple steady-state bifurcation thresholds. Then, we use weak nonlinear analysis to derive amplitude equations to determine the direction of Turing bifurcation on multiple time scales. Finally, numerical simulations check the theoretical analysis results well. It is found that the predator-taxis can induce the occurrence of nonhomogeneous steady-state solution in space.</div></div>","PeriodicalId":50226,"journal":{"name":"Journal of Computational and Applied Mathematics","volume":"464 ","pages":"Article 116542"},"PeriodicalIF":2.1,"publicationDate":"2025-01-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143170293","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
Estimation of the covariance matrix of a Gaussian Markov Random Field under a total positivity constraint
IF 2.1 2区 数学
Journal of Computational and Applied Mathematics Pub Date : 2025-01-30 DOI: 10.1016/j.cam.2025.116543
Juan Baz , Pedro Alonso , Juan Manuel Peña , Raúl Pérez-Fernández
{"title":"Estimation of the covariance matrix of a Gaussian Markov Random Field under a total positivity constraint","authors":"Juan Baz ,&nbsp;Pedro Alonso ,&nbsp;Juan Manuel Peña ,&nbsp;Raúl Pérez-Fernández","doi":"10.1016/j.cam.2025.116543","DOIUrl":"10.1016/j.cam.2025.116543","url":null,"abstract":"<div><div>Gaussian Markov Random Fields are a popular statistical model that has been used successfully in many fields of application. Recent work has studied conditions under which the covariance matrix of a Gaussian Markov Random Field over a graph of paths is totally positive. In such case, many linear algebra operations concerning the covariance matrix can be performed with High Relative Accuracy (the relative error is of order of machine precision). Unfortunately, classical estimators of the covariance matrix do not necessarily yield a totally positive matrix, even when the population covariance matrix is totally positive. Essentially, this inconvenience prevents the available High Relative Accuracy methods to be used with real-life data. Here, we present a method for the estimation of the covariance matrix of a Gaussian Markov Random Field over a graph of paths assuring the estimated covariance matrix (or its inverse) is totally positive.</div></div>","PeriodicalId":50226,"journal":{"name":"Journal of Computational and Applied Mathematics","volume":"464 ","pages":"Article 116543"},"PeriodicalIF":2.1,"publicationDate":"2025-01-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143170288","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 matrix eigenvalue–eigenvector equality for semi-simple eigenvalues
IF 2.1 2区 数学
Journal of Computational and Applied Mathematics Pub Date : 2025-01-26 DOI: 10.1016/j.cam.2025.116520
Huijian Zhu , Jiawen Ding , Jiu Ding
{"title":"A matrix eigenvalue–eigenvector equality for semi-simple eigenvalues","authors":"Huijian Zhu ,&nbsp;Jiawen Ding ,&nbsp;Jiu Ding","doi":"10.1016/j.cam.2025.116520","DOIUrl":"10.1016/j.cam.2025.116520","url":null,"abstract":"<div><div>For a complex square matrix, we present an eigenvalue–eigenvector equality for its semi-simple eigenvalue with a basis of the corresponding eigenspace under the condition that the eigenspace is orthogonal to eigenspaces or generalized eigenspaces corresponding to all other eigenvalues of the matrix. As a special case, we obtain a generalized eigenvector–eigenvalue-identity for the eigenvalue with an orthonormal basis of the eigenspace, which generalizes the well-known eigenvector–eigenvalue identity for a simple eigenvalue of normal matrices. We also give an application of the new formula to Jacobi matrices.</div></div>","PeriodicalId":50226,"journal":{"name":"Journal of Computational and Applied Mathematics","volume":"464 ","pages":"Article 116520"},"PeriodicalIF":2.1,"publicationDate":"2025-01-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143170296","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 efficient inertial projection-based algorithm for constrained nonlinear pseudo-monotone equations and its application to logistic regression problems
IF 2.1 2区 数学
Journal of Computational and Applied Mathematics Pub Date : 2025-01-24 DOI: 10.1016/j.cam.2025.116532
Yong-Yan Yue , Teng-Teng Yao , Xiao-Qing Jin , Zhi Zhao
{"title":"An efficient inertial projection-based algorithm for constrained nonlinear pseudo-monotone equations and its application to logistic regression problems","authors":"Yong-Yan Yue ,&nbsp;Teng-Teng Yao ,&nbsp;Xiao-Qing Jin ,&nbsp;Zhi Zhao","doi":"10.1016/j.cam.2025.116532","DOIUrl":"10.1016/j.cam.2025.116532","url":null,"abstract":"<div><div>The problem of solving nonlinear pseudo-monotone equations with convex constraints is studied in this paper. To solve this problem, an adaptive hyperplane projection method is proposed. At each iteration, a diagonal Barzilai–Borwein method is used to construct search direction. For the hyperplane projection step, an extrapolation step is applied by using a nonmonotone line search technique. In addition, an inertial technique is applied for possible acceleration of this new algorithm. Under the assumptions that the underlying map is continuous and the solution set is nonempty, the proposed new algorithm is globally convergent. Moreover, if the Lipschitz continuity condition and the local error bound condition are also satisfied, then the new algorithm has a local linear convergence rate. Numerical experiments are reported to show the efficiency of the proposed method.</div></div>","PeriodicalId":50226,"journal":{"name":"Journal of Computational and Applied Mathematics","volume":"464 ","pages":"Article 116532"},"PeriodicalIF":2.1,"publicationDate":"2025-01-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143169626","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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