Article
Mathematics
Rabiu Bashir Yunus, Nooraini Zainuddin, Hanita Daud, Ramani Kannan, Samsul Ariffin Abdul Karim, Mahmoud Muhammad Yahaya
Summary: This paper proposes a modification to the HS method by using a spectral parameter based on a modified secant relation. The proposed method does not require a safeguarding strategy and ensures a positive and definite Hessian matrix throughout the iteration process. Numerical experiments on various test problems validate the effectiveness of the proposed algorithm compared to existing techniques, and favorable outcomes are observed in motion-control problems in a robotic model.
Article
Operations Research & Management Science
Brian Irwin, Eldad Haber
Summary: In this paper, a new variant of the BFGS method called Secant Penalized BFGS (SP-BFGS) is introduced to handle noise in gradient measurements. By treating the secant condition with a penalty method approach, a parametric family is generated, allowing for different degrees of updating the inverse Hessian approximation. SP-BFGS provides a means to incrementally update the inverse Hessian approximation with controlled bias, resisting the detrimental effects of noise and negative curvature measurements.
COMPUTATIONAL OPTIMIZATION AND APPLICATIONS
(2023)
Article
Mathematics, Applied
Mahmoud Muhammad Yahaya, Poom Kumam, Aliyu Muhammed Awwal, Sani Aji
Summary: This article proposes a structured diagonal Hessian approximation for solving non-linear least-squares problems, deriving the formulation through solving a minimization problem. Experimental results demonstrate the effectiveness of the proposed algorithm, showing its applicability in the motion control of planar robots.
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS
(2021)
Article
Mathematics, Applied
Federica Pes, Giuseppe Rodriguez
Summary: This paper focuses on the computation of the minimal-norm solution for an underdetermined nonlinear least-squares problem, presenting a Gauss-Newton method with two relaxation parameters for convergence assurance. The method also includes a dynamic estimation process for the parameters and rank of the Jacobian matrix.
APPLIED NUMERICAL MATHEMATICS
(2022)
Article
Mathematics, Applied
Basim A. Hassan, Issam A. R. Moghrabi
Summary: One of the most prominent iterative approaches for solving unconstrained optimization problems is the quasi-Newton method, which is known for its fast convergence and exceptional precision. This article proposes a modified secant relation based on a quadratic model to better approximate the objective function's second curvature. A new BFGS method is then introduced for resolving unconstrained optimization problems using this modified secant relationship. The proposed method utilizes both gradient and function values, leading to global convergence without requiring any convexity assumption on the objective function. Comparative results demonstrate the computational efficiency of the proposed method in terms of iteration count and function/gradient evaluations.
JOURNAL OF APPLIED MATHEMATICS AND COMPUTING
(2023)
Article
Computer Science, Software Engineering
Nicolas Boutet, Joris Degroote, Rob Haelterman
Summary: This paper investigates how to find an estimate of the Jacobian matrix as close as possible to the real matrix in quasi-Newton methods. The author proposes a method that combines multi-secant and symmetric methods into a single update formula. The novelty of this method lies in grouping and ordering secant equations based on their relative importance. The method can be applied in various applications involving multiple secant equations.
OPTIMIZATION METHODS & SOFTWARE
(2022)
Article
Computer Science, Interdisciplinary Applications
Ji Hee Kim, Naeun Choi, Seongmin Heo
Summary: This work proposes a novel iterative least squares method to approximate nonlinear functions using constrained least squares to ensure continuity. The method improves upon the existing continuous piecewise linear (CPWL) method by modifying the main steps and employing partitioned least squares and constrained least squares to reduce computational complexity. An iterative procedure with gradient descent using momentum is used for breakpoint updates to improve convergence characteristics.
COMPUTERS & CHEMICAL ENGINEERING
(2022)
Review
Engineering, Mechanical
Randall J. Allemang, Rohit S. Patwardhan, Murali M. Kolluri, Allyn W. Phillips
Summary: This paper outlines various FRF estimation techniques and compares algorithms that compute FRF using different methods. It also discusses inconsistencies in some conditioned coherence metrics and provides corrected interpretations.
MECHANICAL SYSTEMS AND SIGNAL PROCESSING
(2022)
Article
Mathematics, Applied
Saman Babaie-Kafaki, Zohre Aminifard, Saeide Ghafoori
Summary: In this paper, a memoryless symmetric rank-one quasi-Newton method is proposed, which imposes a rank-one modification on an adaptively scaled version of the identity matrix. By appropriately combining the given updating formula with the well-known DFP quasi-Newton updating formula, positive definiteness is guaranteed, and descent directions are generated. The convergence analysis of the hybrid method is carried out. Eventually, the practical advantage of the method is numerically appraised through some CUTEr problems as well as the sparse recovery problem.
COMPUTATIONAL & APPLIED MATHEMATICS
(2022)
Article
Mathematics, Applied
Zhi Zhao, Xiao-Qing Jin, Teng-Teng Yao
Summary: This paper focuses on the parameterized least squares inverse eigenvalue problems and proposes a method based on Riemannian manifold and Euclidean space for solving the corresponding nonlinear least squares problem. The convergence and convergence rate of the algorithm are discussed, and numerical experiments demonstrate its efficiency.
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS
(2022)
Article
Computer Science, Information Systems
Mahmoud Muhammad Yahaya, Poom Kumam, Aliyu Muhammed Awwal, Parin Chaipunya, Sani Aji, Sani Salisu
Summary: This study presents a generalized structured-based diagonal Hessian algorithm for solving nonlinear least-squares problems. It extends the existing method and demonstrates its effectiveness through experimental testing and application to robotic motion control.
Article
Mathematics, Applied
Leonardo A. Sousa, Susana Scheimberg, Pedro Jorge S. Santos, Paulo Sergio M. Santos
Summary: In this work, a quasi-Newton-type method for equilibrium problems is developed based on the proximal Newton-type structure. The algorithm's sequence is proven to be well defined and under appropriate assumptions, linear convergence is established. Numerical experiments were conducted to verify the effectiveness of the method.
NUMERICAL ALGORITHMS
(2022)
Article
Engineering, Electrical & Electronic
Wanjin Feng, Jianyu Fu, Ying Hou, Chao Liu, Peng Huang, Dapeng Chen
Summary: In this work, a projection transformation method suitable for small-scale networked thermopile arrays is proposed to eliminate crosstalk and reconstruct thermal images accurately.
IEEE SENSORS JOURNAL
(2022)
Article
Mathematics
Luis Alberto Cantera-Cantera, Cristobal Vargas-Jarillo, Sergio Isai Palomino-Resendiz, Yair Lozano-Hernandez, Carlos Manuel Montelongo-Vazquez
Summary: This article introduces the classical curve-fitting problem and the related methods of least squares, total least squares, and orthogonal distances. The research shows that TLS and OD methods yield the same estimates when fitting a first-degree polynomial without an independent coefficient.
Article
Multidisciplinary Sciences
Mahmoud Muhammad Yahaya, Poom Kumam, Aliyu Muhammed Awwal, Sani Aji
Summary: This study proposes three structured spectral gradient algorithms based on the spectral parameters of Barzillai and Borwein (1998) for solving NLS problems. By incorporating structured gradient and information from structured Hessian approximation, the algorithms are shown to be globally convergent with the use of a nonmonotone line-search strategy. Experimental results demonstrate the efficiency of the proposed algorithms.
Article
Computer Science, Artificial Intelligence
Ichraf Lahouli, Evangelos Karakasis, Robby Haelterman, Zied Chtourou, Geert De Cubber, Antonios Gasteratos, Rabah Attia
IET IMAGE PROCESSING
(2018)
Article
Thermodynamics
S. Gusev, D. Ziviani, J. Vierendeels, M. De Paepe
INTERNATIONAL JOURNAL OF REFRIGERATION-REVUE INTERNATIONALE DU FROID
(2019)
Article
Engineering, Electrical & Electronic
Mathias Becquaert, Edison Cristofani, Ben Lauwens, Marijke Vandewal, Johan H. Stiens, Nikos Deligiannis
IEEE SENSORS JOURNAL
(2019)
Article
Geochemistry & Geophysics
Michal Shimoni, Rob Haelterman, Christiaan Perneel
IEEE GEOSCIENCE AND REMOTE SENSING MAGAZINE
(2019)
Article
Operations Research & Management Science
Nicolas Boutet, Rob Haelterman, Joris Degroote
COMPUTATIONAL OPTIMIZATION AND APPLICATIONS
(2020)
Article
Physics, Fluids & Plasmas
T. Wauters, J. Buermans, R. Haelterman, V Moiseenko, D. Ricci, T. Verhaeghe, S. Coda, D. Douai, A. Hakola, A. Lyssoivan, D. Van Eester
PLASMA PHYSICS AND CONTROLLED FUSION
(2020)
Article
Operations Research & Management Science
Nicolas Boutet, Rob Haelterman, Joris Degroote
Summary: This paper proposes a new update formula for the estimate of the Hessian matrix in optimization, called generalised PSB (gPSB), which combines the Powell-Symetric-Broyden formula with information from previous optimization steps. The study provides a novel interpretation of the non-existence of gPSB and compares it with other methods to show its advantages in estimating the Hessian matrix.
COMPUTATIONAL OPTIMIZATION AND APPLICATIONS
(2021)
Article
Chemistry, Analytical
Sofia Scataglini, Stijn Verwulgen, Eddy Roosens, Robby Haelterman, Damien Van Tiggelen
Summary: This study compared spatiotemporal gait parameters in 19 subjects using two different systems, finding differences in SPT between them with OptoGait showing a smaller error. Accurate detection of heel strike and toe-off was found to significantly impact the entire data acquisition.
Article
Mathematics, Applied
Julien Petit, Renaud Lambiotte, Timoteo Carletti
Summary: Graph-limit theory focuses on the convergence of sequences of increasingly large graphs, providing a framework for studying dynamical systems on massive graphs where traditional methods would become computationally intractable. By approximating standard ordinary differential equations with nonlocal evolution equations on the unit interval, this methodology is employed to prove the validity of the continuum limit of random walks. The theory is applied to two classes of processes on dense weighted graphs, in discrete and continuous time, with dynamics encoded in transition matrices or random-walk Laplacians.
SIAM JOURNAL ON APPLIED MATHEMATICS
(2021)
Proceedings Paper
Engineering, Industrial
Sofia Scataglini, Guillaume Abran, Eddy Roosens, Damien Van Tiggelen, Robby Haelterman, Stijn Verwulgen
PROCEEDINGS OF THE 6TH INTERNATIONAL DIGITAL HUMAN MODELING SYMPOSIUM (DHM2020)
(2020)
Proceedings Paper
Computer Science, Artificial Intelligence
Janne Heirman, Shivam Selleri, Tom De Vleeschauwer, Charles Hamesse, Michel Bellemans, Evarest Schoofs, Rob Haelterman
2020 IEEE INTERNATIONAL CONFERENCE ON ARTIFICIAL INTELLIGENCE AND VIRTUAL REALITY (AIVR 2020)
(2020)
Proceedings Paper
Automation & Control Systems
Geert De Cubber, Rob Haelterman
2019 IEEE INTERNATIONAL SYMPOSIUM ON MEASUREMENT AND CONTROL IN ROBOTICS (ISMCR): ROBOTICS FOR THE BENEFIT OF HUMANITY
(2019)
Article
Computer Science, Theory & Methods
Julien Petit, Renaud Lambiotte, Timoteo Carletti
APPLIED NETWORK SCIENCE
(2019)
Proceedings Paper
Computer Science, Artificial Intelligence
Sofia Scataglini, Femke Danckaers, Robby Haelterman, Toon Huysmans, Jan Sijbers, Giuseppe Andreoni
PROCEEDINGS OF THE 20TH CONGRESS OF THE INTERNATIONAL ERGONOMICS ASSOCIATION (IEA 2018), VOL V: HUMAN SIMULATION AND VIRTUAL ENVIRONMENTS, WORK WITH COMPUTING SYSTEMS (WWCS), PROCESS CONTROL
(2019)
Proceedings Paper
Computer Science, Artificial Intelligence
Sofia Scataglini, Femke Danckaers, Robby Haelterman, Toon Huysmans, Jan Sijbers
PROCEEDINGS OF THE 20TH CONGRESS OF THE INTERNATIONAL ERGONOMICS ASSOCIATION (IEA 2018), VOL V: HUMAN SIMULATION AND VIRTUAL ENVIRONMENTS, WORK WITH COMPUTING SYSTEMS (WWCS), PROCESS CONTROL
(2019)
Article
Mathematics, Applied
M. S. Bruzon, T. M. Garrido, R. de la Rosa
Summary: We study a family of generalized Zakharov-Kuznetsov modified equal width equations in (2+1)-dimensions involving an arbitrary function and three parameters. By using the Lie group theory, we classify the Lie point symmetries of these equations and obtain exact solutions. We also show that this family of equations admits local low-order multipliers and derive all local low-order conservation laws through the multiplier approach.
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS
(2024)
Article
Mathematics, Applied
Dohee Jung, Changbum Chun
Summary: The paper presents a general approach to enhance the Pade iterations for computing the matrix sign function by selecting an arbitrary three-point family of methods based on weight functions. The approach leads to a multi-parameter family of iterations and allows for the discovery of new methods. Convergence and stability analysis as well as numerical experiments confirm the improved performance of the new methods.
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS
(2024)
Article
Mathematics, Applied
Abhishek Yadav, Amit Setia, M. Thamban Nair
Summary: In this paper, we propose a Galerkin's residual-based numerical scheme for solving a system of Cauchy-type singular integral equations using Chebyshev polynomials. We prove the well-posedness of the system and derive a theoretical error bound and convergence order. The numerical examples validate the theoretical results.
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS
(2024)
Article
Mathematics, Applied
Fernando Chacon-Gomez, M. Eugenia Cornejo, Jesus Medina, Eloisa Ramirez-Poussa
Summary: The use of decision rules allows for reliable extraction of information and inference of conclusions from relational databases, but the concepts of decision algorithms need to be extended in fuzzy environments.
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS
(2024)
Article
Mathematics, Applied
Ilhame Amirali, Gabil M. Amiraliyev
Summary: This paper considers the one-dimensional initial-boundary problem for a pseudoparabolic equation with a time delay. To solve this problem numerically, a higher-order difference method is constructed and the error estimate for its solution is obtained. Based on the method of energy estimates, the fully discrete scheme is shown to be convergent of order four in space and of order two in time. The given numerical results illustrate the convergence and effectiveness of the numerical method.
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS
(2024)
Article
Mathematics, Applied
Tong-tong Shang, Guo-ji Tang, Wen-sheng Jia
Summary: The goal of this paper is to investigate a class of linear complementarity problems over tensor-spaces, denoted by TLCP, which is an extension of the classical linear complementarity problem. First, two classes of structured tensors over tensor-spaces (i.e., T-R tensor and T-RO tensor) are introduced and some equivalent characterizations are discussed. Then, the lower bound and upper bound of the solutions in the sense of the infinity norm of the TLCP are obtained when the problem has a solution.
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS
(2024)
Article
Mathematics, Applied
Fabio Difonzo, Pawel Przybylowicz, Yue Wu
Summary: This paper focuses on the existence, uniqueness, and approximation of solutions of delay differential equations (DDEs) with Caratheodory type right-hand side functions. It presents the construction of the randomized Euler scheme for DDEs and investigates its error. Furthermore, the paper reports the results of numerical experiments.
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS
(2024)
Article
Mathematics, Applied
Priyanka Roy, Geetanjali Panda, Dong Qiu
Summary: In this article, a gradient based descent line search scheme is proposed for solving interval optimization problems under generalized Hukuhara differentiability. The innovation and importance of these concepts are presented from practical and computational perspectives. The necessary condition for existence of critical point is presented in inclusion form of interval-valued gradient. Suitable efficient descent direction is chosen based on the monotonic property of the interval-valued function and specific interval ordering. Mathematical convergence of the scheme is proved under the assumption of Inexact line search. The theoretical developments are implemented with a set of interval test problems in different dimensions. A possible application in finance is provided and solved by the proposed scheme.
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS
(2024)
Article
Mathematics, Applied
Zhongqian Wang, Changqing Ye, Eric T. Chung
Summary: In this paper, the constrained energy minimizing generalized multiscale finite element method (CEM-GMsFEM) with mixed boundary conditions for elasticity equations in high contrast media is developed. The method offers advantages such as independence of target region's contrast from precision and significant impact of oversampling domain sizes on numerical accuracy. Furthermore, this is the first proof of convergence of CEM-GMsFEM with mixed boundary conditions for elasticity equations. Numerical experiments demonstrate the method's performance.
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS
(2024)
Article
Mathematics, Applied
Samaneh Soradi-Zeid, Maryam Alipour
Summary: The Laguerre polynomials are a new set of basic functions used to solve a specific class of optimal control problems specified by integro-differential equations, namely IOCP. The corresponding operational matrices of derivatives are calculated to extend the solution of the problem in terms of Laguerre polynomials. By considering the basis functions and using the collocation method, the IOCP is simplified into solving a system of nonlinear algebraic equations. The proposed method has been proven to have an error bound and convergence analysis for the approximate optimal value of the performance index. Finally, examples are provided to demonstrate the validity and applicability of this technique.
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS
(2024)
Article
Mathematics, Applied
Almudena P. Marquez, Maria L. Gandarias, Stephen C. Anco
Summary: A generalization of the KP equation involving higher-order dispersion is studied. The Lie point symmetries and conservation laws of the equation are obtained using Noether's theorem and the introduction of a potential. Sech-type line wave solutions are found and their features, including dark solitary waves on varying backgrounds, are discussed.
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS
(2024)
Article
Mathematics, Applied
Susanne Saminger-Platz, Anna Kolesarova, Adam Seliga, Radko Mesiar, Erich Peter Klement
Summary: In this article, we study real functions defined on the unit square satisfying basic properties and explore the conditions for generating bivariate copulas using parameterized transformations and other constructions.
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS
(2024)
Article
Mathematics, Applied
Lulu Tian, Nattaporn Chuenjarern, Hui Guo, Yang Yang
Summary: In this paper, a new local discontinuous Galerkin (LDG) algorithm is proposed to solve the incompressible Euler equation in two dimensions on overlapping meshes. The algorithm solves the vorticity, velocity field, and potential function on different meshes. The method employs overlapping meshes to ensure continuity of velocity along the interfaces of the primitive meshes, allowing for the application of upwind fluxes. The article introduces two sufficient conditions to maintain the maximum principle of vorticity.
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS
(2024)
Article
Mathematics, Applied
Cheng Wang, Jilu Wang, Steven M. Wise, Zeyu Xia, Liwei Xu
Summary: In this paper, a temporally second-order accurate numerical scheme for the Cahn-Hilliard-Magnetohydrodynamics system of equations is proposed and analyzed. The scheme utilizes a modified Crank-Nicolson-type approximation for time discretization and a mixed finite element method for spatial discretization. The modified Crank-Nicolson approximation allows for mass conservation and energy stability analysis. Error estimates are derived for the phase field, velocity, and magnetic fields, and numerical examples are presented to validate the proposed scheme's theoretical results.
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS
(2024)
Article
Mathematics, Applied
Mingyu He, Wenyuan Liao
Summary: This paper presents a numerical method for solving reaction-diffusion equations in spatially heterogeneous domains, which are commonly used to model biological applications. The method utilizes a fourth-order compact alternative directional implicit scheme based on Pade approximation-based operator splitting techniques. Stability analysis shows that the method is unconditionally stable, and numerical examples demonstrate its high efficiency and high order accuracy in both space and time.
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS
(2024)
