Pub Date : 2026-10-01Epub Date: 2026-02-26DOI: 10.1016/j.cam.2026.117465
Massimo Costabile, Emilio Russo, Fabio Viviano
The paper proposes a lattice-based approximation for pricing bonds and interest-sensitive claims when short-term interest rates fluctuate according to an Ornstein-Uhlenbeck process with the sticky reflecting boundary at zero. The framework is of particular interest when central banks adopt zero interest rate policies, e.g., the US monetary policy response to the financial crisis in 2008. The proposed model provides an evaluation instrument, useful for practitioners too, that is able to manage easily the sticky reflecting feature, thus avoiding to resort to the complex evaluation formulas that can arise when embedding such a feature in the considered dynamics. The underlying interest rate process is discretized through a recombining binomial lattice in which the number of nodes grows up linearly with the number of time steps. The resulting algorithm is applied to evaluate bonds and interest-sensitive claims in order to show its accuracy and efficiency.
{"title":"Efficient pricing of interest rate derivatives under a sticky diffusion","authors":"Massimo Costabile, Emilio Russo, Fabio Viviano","doi":"10.1016/j.cam.2026.117465","DOIUrl":"10.1016/j.cam.2026.117465","url":null,"abstract":"<div><div>The paper proposes a lattice-based approximation for pricing bonds and interest-sensitive claims when short-term interest rates fluctuate according to an Ornstein-Uhlenbeck process with the sticky reflecting boundary at zero. The framework is of particular interest when central banks adopt zero interest rate policies, e.g., the US monetary policy response to the financial crisis in 2008. The proposed model provides an evaluation instrument, useful for practitioners too, that is able to manage easily the sticky reflecting feature, thus avoiding to resort to the complex evaluation formulas that can arise when embedding such a feature in the considered dynamics. The underlying interest rate process is discretized through a recombining binomial lattice in which the number of nodes grows up linearly with the number of time steps. The resulting algorithm is applied to evaluate bonds and interest-sensitive claims in order to show its accuracy and efficiency.</div></div>","PeriodicalId":50226,"journal":{"name":"Journal of Computational and Applied Mathematics","volume":"484 ","pages":"Article 117465"},"PeriodicalIF":2.6,"publicationDate":"2026-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147386999","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 : 2026-10-01Epub Date: 2026-02-26DOI: 10.1016/j.cam.2026.117521
Janez Puhan, Árpád Bűrmen
The paper outlines the derivation of optimal parameter values for the Nelder–Mead simplex algorithm as a function of the optimization problem’s dimension. The derivation applies to a general, strictly convex quadratic objective function, under the assumption that the simplex’s centroid probability density function within the ellipsoid defined by the simplex’s worst vertex is independent of the centroid’s distance to the worst vertex. The derived dependences of the Nelder–Mead simplex algorithm parameters show similarities with the heuristic solutions proposed so far. The algorithm’s performance, relative to its default parameter settings, was tested on a quadratic function in 10, 20, 50, and 100 dimensions.
{"title":"On the optimal parameter values of the Nelder–Mead simplex algorithm","authors":"Janez Puhan, Árpád Bűrmen","doi":"10.1016/j.cam.2026.117521","DOIUrl":"10.1016/j.cam.2026.117521","url":null,"abstract":"<div><div>The paper outlines the derivation of optimal parameter values for the Nelder–Mead simplex algorithm as a function of the optimization problem’s dimension. The derivation applies to a general, strictly convex quadratic objective function, under the assumption that the simplex’s centroid probability density function within the ellipsoid defined by the simplex’s worst vertex is independent of the centroid’s distance to the worst vertex. The derived dependences of the Nelder–Mead simplex algorithm parameters show similarities with the heuristic solutions proposed so far. The algorithm’s performance, relative to its default parameter settings, was tested on a quadratic function in 10, 20, 50, and 100 dimensions.</div></div>","PeriodicalId":50226,"journal":{"name":"Journal of Computational and Applied Mathematics","volume":"484 ","pages":"Article 117521"},"PeriodicalIF":2.6,"publicationDate":"2026-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147387002","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 : 2026-10-01Epub Date: 2026-02-18DOI: 10.1016/j.cam.2026.117462
Imen Ferjani
In this work, we study relatively generalized weakly demicompact (GWMD) operators on Banach spaces, a class that extends several compactness-type notions used in operator theory and applications. We give a new characterization of GWMD operators using the De Blasi measure of noncompactness and related weak noncompactness measures, yielding practical criteria for verifying this property. We also prove that the GWMD operators are stable under a class of perturbations. Next, we analyze 2 × 2 block operator matrices and derive simple conditions under which the full block matrix is GWMD. To illustrate the theoretical results, numerical experiments are conducted for weighted-shift and Volterra-type operators using finite-dimensional truncations and finite element discretizations. The experiments confirm the predicted stability and spectral decay behavior, showing that the theoretical properties persist under numerical approximation.
{"title":"Characterization and numerical simulations of relative generalized weak demicompact operators","authors":"Imen Ferjani","doi":"10.1016/j.cam.2026.117462","DOIUrl":"10.1016/j.cam.2026.117462","url":null,"abstract":"<div><div>In this work, we study relatively generalized weakly demicompact (GWMD) operators on Banach spaces, a class that extends several compactness-type notions used in operator theory and applications. We give a new characterization of GWMD operators using the De Blasi measure of noncompactness and related weak noncompactness measures, yielding practical criteria for verifying this property. We also prove that the GWMD operators are stable under a class of perturbations. Next, we analyze 2 × 2 block operator matrices and derive simple conditions under which the full block matrix is GWMD. To illustrate the theoretical results, numerical experiments are conducted for weighted-shift and Volterra-type operators using finite-dimensional truncations and finite element discretizations. The experiments confirm the predicted stability and spectral decay behavior, showing that the theoretical properties persist under numerical approximation.</div></div>","PeriodicalId":50226,"journal":{"name":"Journal of Computational and Applied Mathematics","volume":"484 ","pages":"Article 117462"},"PeriodicalIF":2.6,"publicationDate":"2026-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147386623","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 : 2026-10-01Epub Date: 2026-02-21DOI: 10.1016/j.cam.2026.117502
Nguyen Van Hung , Nguyen Huynh Vu Duy , Jen Chih Yao , Shengda Zeng
The goal of this paper is to study the convergence analysis of solution sets to fuzzy weak vector quasi-equilibrium problems. Firstly, we introduce some weak vector quasi-equilibrium problems in fuzzy environment. Secondly, we establish several sufficient conditions for the upper convergence for these problems. Thirdly, the auxiliary subsets of solution sets to fuzzy weak vector quasi-equilibrium problems and the concept of weakly K-quasi-concavity of the objective function are obtained. Results on the lower convergence and convergence of the solution sets based on the auxiliary subsets and the concept of weakly K-quasi-concavity for fuzzy weak vector quasi-equilibrium problems are established and studied. Finally, as an application, we consider the upper convergence, lower convergence and convergence of the solution sets of fuzzy vector quasi-optimization problems. Our results in this paper are new and different from some main results in the literature. Many examples are given for the illustration of our results.
{"title":"Convergence analysis of solutions to fuzzy weak vector quasi-equilibrium problems and applications","authors":"Nguyen Van Hung , Nguyen Huynh Vu Duy , Jen Chih Yao , Shengda Zeng","doi":"10.1016/j.cam.2026.117502","DOIUrl":"10.1016/j.cam.2026.117502","url":null,"abstract":"<div><div>The goal of this paper is to study the convergence analysis of solution sets to fuzzy weak vector quasi-equilibrium problems. Firstly, we introduce some weak vector quasi-equilibrium problems in fuzzy environment. Secondly, we establish several sufficient conditions for the upper convergence for these problems. Thirdly, the auxiliary subsets of solution sets to fuzzy weak vector quasi-equilibrium problems and the concept of weakly <em>K</em>-quasi-concavity of the objective function are obtained. Results on the lower convergence and convergence of the solution sets based on the auxiliary subsets and the concept of weakly <em>K</em>-quasi-concavity for fuzzy weak vector quasi-equilibrium problems are established and studied. Finally, as an application, we consider the upper convergence, lower convergence and convergence of the solution sets of fuzzy vector quasi-optimization problems. Our results in this paper are new and different from some main results in the literature. Many examples are given for the illustration of our results.</div></div>","PeriodicalId":50226,"journal":{"name":"Journal of Computational and Applied Mathematics","volume":"484 ","pages":"Article 117502"},"PeriodicalIF":2.6,"publicationDate":"2026-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147386629","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 : 2026-10-01Epub Date: 2026-02-24DOI: 10.1016/j.cam.2026.117540
Danilo Costarelli, Michele Piconi
In this paper, we provide two algorithms based on the theory of multidimensional neural network (NN) operators activated by hyperbolic tangent sigmoidal functions. Theoretical results are recalled to justify the performance of the here implemented algorithms. Specifically, the first algorithm models multidimensional signals (such as digital images), while the second one addresses the problem of rescaling and enhancement of the considered data. The asymptotic computational complexity of the proposed algorithms is also analyzed. Several applications of the NN-based algorithms for modeling and rescaling/enhancement remote sensing data (represented as images) are discussed, together with numerical experiments conducted on a selection of remote sensing (RS) images from the (open access) RETINA dataset. A comparison with classical interpolation methods, such as bilinear and bicubic interpolation, shows that the proposed algorithms outperform the others, particularly in terms of the Structural Similarity Index (SSIM).
{"title":"Implementation of neural network operators with applications to remote sensing data","authors":"Danilo Costarelli, Michele Piconi","doi":"10.1016/j.cam.2026.117540","DOIUrl":"10.1016/j.cam.2026.117540","url":null,"abstract":"<div><div>In this paper, we provide two algorithms based on the theory of multidimensional neural network (NN) operators activated by hyperbolic tangent sigmoidal functions. Theoretical results are recalled to justify the performance of the here implemented algorithms. Specifically, the first algorithm models multidimensional signals (such as digital images), while the second one addresses the problem of rescaling and enhancement of the considered data. The asymptotic computational complexity of the proposed algorithms is also analyzed. Several applications of the NN-based algorithms for modeling and rescaling/enhancement remote sensing data (represented as images) are discussed, together with numerical experiments conducted on a selection of remote sensing (RS) images from the (open access) RETINA dataset. A comparison with classical interpolation methods, such as bilinear and bicubic interpolation, shows that the proposed algorithms outperform the others, particularly in terms of the Structural Similarity Index (SSIM).</div></div>","PeriodicalId":50226,"journal":{"name":"Journal of Computational and Applied Mathematics","volume":"484 ","pages":"Article 117540"},"PeriodicalIF":2.6,"publicationDate":"2026-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147386636","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 : 2026-10-01Epub Date: 2026-02-25DOI: 10.1016/j.cam.2026.117530
Wenli Yang
We propose a novel method for fusing infrared and visible images, which integrates a first-order piecewise regularization and an inertial proximal alternating direction method of multipliers (IPADMM). Our model consists of two fidelity terms and one first-order piecewise regularization term, which effectively preserve both the thermal radiation information in the infrared image and the appearance information in the visible image. The inclusion of the first-order piecewise regularization term reduces the staircase effect and enhances the preservation of sharp edges. We also discuss the maximum-minimum principle of the model with Neumann boundary conditions. To minimize the proposed model, we propose an IPADMM-based fast algorithm and establish its convergence analysis. Furthermore, we conduct numerical experiments to highlight the distinctive features of our model and compare it with other image fusion techniques.
{"title":"Infrared and visible image fusion via a first-order piecewise regularization and an IPADMM","authors":"Wenli Yang","doi":"10.1016/j.cam.2026.117530","DOIUrl":"10.1016/j.cam.2026.117530","url":null,"abstract":"<div><div>We propose a novel method for fusing infrared and visible images, which integrates a first-order piecewise regularization and an inertial proximal alternating direction method of multipliers (IPADMM). Our model consists of two fidelity terms and one first-order piecewise regularization term, which effectively preserve both the thermal radiation information in the infrared image and the appearance information in the visible image. The inclusion of the first-order piecewise regularization term reduces the staircase effect and enhances the preservation of sharp edges. We also discuss the maximum-minimum principle of the model with Neumann boundary conditions. To minimize the proposed model, we propose an IPADMM-based fast algorithm and establish its convergence analysis. Furthermore, we conduct numerical experiments to highlight the distinctive features of our model and compare it with other image fusion techniques.</div></div>","PeriodicalId":50226,"journal":{"name":"Journal of Computational and Applied Mathematics","volume":"484 ","pages":"Article 117530"},"PeriodicalIF":2.6,"publicationDate":"2026-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147386639","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 : 2026-10-01Epub Date: 2026-02-13DOI: 10.1016/j.cam.2026.117401
Eduardo Abreu , Paola Ferraz , Jean Renel François , Juan Galvis
We study computational strategies for solving elliptic-pressure-velocity models in high-contrast multiscale flow problems involving two- and three-phase incompressible flow in heterogeneous porous media. Such problems arise in many subsurface applications, including oil recovery and groundwater management. Numerical simulation of these flows is challenging due to the strong heterogeneity of the permeability field, the nonlinear coupling between pressure and saturation equations, and the need to resolve fine-scale features that influence macroscopic behavior. To address these challenges, we employ a coupled multiscale framework that integrates the Generalized Multiscale Finite Element Method (GMsFEM) for the elliptic pressure-velocity equation with a recently introduced semi-discrete Lagrangian-Eulerian formulation for the hyperbolic transport equations. The GMsFEM efficiently captures fine-scale heterogeneities through localized spectral basis functions on a coarse grid, significantly reducing computational cost. Meanwhile, the semi-discrete Lagrangian-Eulerian method is well suited for advective-dominated transport and provides high-resolution solutions for saturation evolution. Coupling these two numerical strategies-each optimized for a different class of equations-is non-trivial. It requires careful handling of information transfer between the coarse-scale pressure approximation and the fine-scale transport solver to ensure both stability and accuracy. We design and validate such a coupling, demonstrating its robustness across a range of challenging test cases. Through numerical experiments on benchmark two-phase and three-phase flow problems, we demonstrate that the proposed methodology captures key multiscale dynamics. These results confirm the effectiveness and versatility of the coupled GMsFEM-Lagrangian-Eulerian approach for large-scale porous media flow simulations.
{"title":"Integrating semi-discrete Lagrangian-Eulerian schemes with generalized multiscale finite elements for enhanced two- and three-phase flow simulations","authors":"Eduardo Abreu , Paola Ferraz , Jean Renel François , Juan Galvis","doi":"10.1016/j.cam.2026.117401","DOIUrl":"10.1016/j.cam.2026.117401","url":null,"abstract":"<div><div>We study computational strategies for solving elliptic-pressure-velocity models in high-contrast multiscale flow problems involving two- and three-phase incompressible flow in heterogeneous porous media. Such problems arise in many subsurface applications, including oil recovery and groundwater management. Numerical simulation of these flows is challenging due to the strong heterogeneity of the permeability field, the nonlinear coupling between pressure and saturation equations, and the need to resolve fine-scale features that influence macroscopic behavior. To address these challenges, we employ a coupled multiscale framework that integrates the Generalized Multiscale Finite Element Method (GMsFEM) for the elliptic pressure-velocity equation with a recently introduced semi-discrete Lagrangian-Eulerian formulation for the hyperbolic transport equations. The GMsFEM efficiently captures fine-scale heterogeneities through localized spectral basis functions on a coarse grid, significantly reducing computational cost. Meanwhile, the semi-discrete Lagrangian-Eulerian method is well suited for advective-dominated transport and provides high-resolution solutions for saturation evolution. Coupling these two numerical strategies-each optimized for a different class of equations-is non-trivial. It requires careful handling of information transfer between the coarse-scale pressure approximation and the fine-scale transport solver to ensure both stability and accuracy. We design and validate such a coupling, demonstrating its robustness across a range of challenging test cases. Through numerical experiments on benchmark two-phase and three-phase flow problems, we demonstrate that the proposed methodology captures key multiscale dynamics. These results confirm the effectiveness and versatility of the coupled GMsFEM-Lagrangian-Eulerian approach for large-scale porous media flow simulations.</div></div>","PeriodicalId":50226,"journal":{"name":"Journal of Computational and Applied Mathematics","volume":"484 ","pages":"Article 117401"},"PeriodicalIF":2.6,"publicationDate":"2026-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147387120","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 : 2026-10-01Epub Date: 2026-02-17DOI: 10.1016/j.cam.2026.117458
Abdüllatif Yalçin , Ebru Karaduman , Ahmet Ocak Akdemir
In this study, we explore symmetric exponentially preinvex functions in the context of conformable fractional calculus. We begin by establishing a new Hermite-Hadamard-Fejér type inequality formulated for this class of functions. In addition, we derive a key fractional integral identity that characterizes the right-hand side of the Hermite-Hadamard inequality under exponential preinvexity. Using this identity–together with the preinvex structure and several classical tools, including Hölder’s inequality and the power-mean inequality–we develop a variety of novel Hermite-Hadamard type estimates involving conformable fractional integrals. These findings provide meaningful extensions to the existing theory of fractional integral inequalities and contribute to the broader analysis of generalized convexity.
{"title":"Fractional integral inequalities for exponentially preinvex functions via conformable fractional integrals","authors":"Abdüllatif Yalçin , Ebru Karaduman , Ahmet Ocak Akdemir","doi":"10.1016/j.cam.2026.117458","DOIUrl":"10.1016/j.cam.2026.117458","url":null,"abstract":"<div><div>In this study, we explore symmetric exponentially preinvex functions in the context of conformable fractional calculus. We begin by establishing a new Hermite-Hadamard-Fejér type inequality formulated for this class of functions. In addition, we derive a key fractional integral identity that characterizes the right-hand side of the Hermite-Hadamard inequality under exponential preinvexity. Using this identity–together with the preinvex structure and several classical tools, including Hölder’s inequality and the power-mean inequality–we develop a variety of novel Hermite-Hadamard type estimates involving conformable fractional integrals. These findings provide meaningful extensions to the existing theory of fractional integral inequalities and contribute to the broader analysis of generalized convexity.</div></div>","PeriodicalId":50226,"journal":{"name":"Journal of Computational and Applied Mathematics","volume":"484 ","pages":"Article 117458"},"PeriodicalIF":2.6,"publicationDate":"2026-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147387123","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 : 2026-10-01Epub Date: 2026-02-14DOI: 10.1016/j.cam.2026.117453
Lennart Duvenbeck, Cedric Riethmüller, Christian Rohde
Restarted GMRES is a robust and widely used iterative solver for linear systems. The control of the restart parameter is a key task to accelerate convergence and to prevent the well-known stagnation phenomenon. We focus on the Proportional-Derivative GMRES (PD-GMRES), which has been derived using control-theoretic ideas in [Cuevas Núñez, Schaerer, and Bhaya (2018)] as a versatile method for modifying the restart parameter. Several variants of a quadtree-based geometric optimization approach are proposed to find a best choice of PD-GMRES parameters. We show that the optimized PD-GMRES performs well across a large number of matrix types and we observe superior performance as compared to major other GMRES-based iterative solvers. Moreover, we propose an extension of the PD-GMRES algorithm to further improve performance by controlling the range of values for the restart parameter.
重新启动GMRES是一种鲁棒且广泛应用于线性系统的迭代求解器。重新启动参数的控制是加速收敛和防止众所周知的停滞现象的关键任务。我们关注的是比例导数GMRES (PD-GMRES)，它是在[Cuevas Núñez， Schaerer, and Bhaya(2018)]中使用控制理论思想导出的，是修改重启参数的通用方法。提出了几种基于四叉树的几何优化方法来寻找PD-GMRES参数的最佳选择。我们表明，优化后的PD-GMRES在大量矩阵类型中表现良好，并且与其他主要的基于gmres的迭代求解器相比，我们观察到优越的性能。此外，我们提出了PD-GMRES算法的扩展，通过控制重启参数的取值范围来进一步提高性能。
{"title":"Data-driven geometric parameter optimization for PD-GMRES","authors":"Lennart Duvenbeck, Cedric Riethmüller, Christian Rohde","doi":"10.1016/j.cam.2026.117453","DOIUrl":"10.1016/j.cam.2026.117453","url":null,"abstract":"<div><div>Restarted GMRES is a robust and widely used iterative solver for linear systems. The control of the restart parameter is a key task to accelerate convergence and to prevent the well-known stagnation phenomenon. We focus on the Proportional-Derivative GMRES (PD-GMRES), which has been derived using control-theoretic ideas in [Cuevas Núñez, Schaerer, and Bhaya (2018)] as a versatile method for modifying the restart parameter. Several variants of a quadtree-based geometric optimization approach are proposed to find a best choice of PD-GMRES parameters. We show that the optimized PD-GMRES performs well across a large number of matrix types and we observe superior performance as compared to major other GMRES-based iterative solvers. Moreover, we propose an extension of the PD-GMRES algorithm to further improve performance by controlling the range of values for the restart parameter.</div></div>","PeriodicalId":50226,"journal":{"name":"Journal of Computational and Applied Mathematics","volume":"484 ","pages":"Article 117453"},"PeriodicalIF":2.6,"publicationDate":"2026-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147387188","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 : 2026-10-01Epub Date: 2026-02-22DOI: 10.1016/j.cam.2026.117501
Guodong Ma, Junji Wang, Jinbao Jian, Wei Zhang
In this paper, we introduce a novel two-step inertial strategy to improve the performance of the conjugate gradient projection method for solving nonlinear monotone equations. Distinct from the existing two-step inertial strategies, the proposed method fully incorporates the two latest iteration points, thereby achieving a more effective utilization of iterative method. Based on the novel two-step inertial strategy, we propose a modified inertial conjugate gradient projection method. We further establish its global convergence and analyze its asymptotic and non-asymptotic convergence rates under the monotonicity and the Lipschitz continuity assumption. Finally, the results of numerical experiments demonstrate that our proposed algorithm has advantages in solving system of nonlinear monotone equations with convex constraints and handling sparse signals and image restoration in compressed sensing.
{"title":"Iteration complexity of a two-step inertial modified CGPM to constrained nonlinear equations for sparse signal and image restoration problems","authors":"Guodong Ma, Junji Wang, Jinbao Jian, Wei Zhang","doi":"10.1016/j.cam.2026.117501","DOIUrl":"10.1016/j.cam.2026.117501","url":null,"abstract":"<div><div>In this paper, we introduce a novel two-step inertial strategy to improve the performance of the conjugate gradient projection method for solving nonlinear monotone equations. Distinct from the existing two-step inertial strategies, the proposed method fully incorporates the two latest iteration points, thereby achieving a more effective utilization of iterative method. Based on the novel two-step inertial strategy, we propose a modified inertial conjugate gradient projection method. We further establish its global convergence and analyze its asymptotic and non-asymptotic convergence rates under the monotonicity and the Lipschitz continuity assumption. Finally, the results of numerical experiments demonstrate that our proposed algorithm has advantages in solving system of nonlinear monotone equations with convex constraints and handling sparse signals and image restoration in compressed sensing.</div></div>","PeriodicalId":50226,"journal":{"name":"Journal of Computational and Applied Mathematics","volume":"484 ","pages":"Article 117501"},"PeriodicalIF":2.6,"publicationDate":"2026-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147386627","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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