Article
Mathematics, Applied
Akira Imakura, Keiichi Morikuni, Akitoshi Takayasu
Summary: We propose a method to compute and verify eigenvalues and corresponding eigenvectors of generalized Hermitian eigenvalue problems in a region. The method uses complex moments and the Rayleigh-Ritz procedure to extract the desired eigencomponents and project the eigenvalue problem into a reduced form. The proposed method enables faster computation and verification of eigenvectors, even for nearly singular matrix pencils and in the presence of multiple and nearly multiple eigenvalues.
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS
(2023)
Article
Physics, Multidisciplinary
Jan Ertl, Michael Marquardt, Moritz Schumacher, Patric Rommel, Joerg Main, Manfred Bayer
Summary: By computing and comparing quantum mechanical and semiclassical recurrence spectra, the study reveals the dynamic characteristics of excitons in cuprous oxide and establishes a direct relationship between the quantum mechanical band structure splittings and classical exciton orbits, providing important insights into exciton physics.
PHYSICAL REVIEW LETTERS
(2022)
Article
Mathematics, Applied
Kensuke Aishima
Summary: Dynamic mode decomposition (DMD) is an efficient analysis method for time series data. This study introduces an adaptive averaging technique to DMD for strong convergence in the statistical sense under a newly constructed noise model. The averaging technique can be generally applied to the new noise model as a preconditioning step, and it is proven that the estimator of the original DMD is inconsistent in the statistical sense.
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS
(2023)
Article
Mathematics, Applied
Yifei Jia, Jiangang Qi, Jing Li
Summary: This paper investigates the optimal recovery of potentials for a Sturm-Liouville problem with only one given eigenvalue. A formula for the infimum of the L1-norm for potential function is obtained, and the attainability of the infimum is specified. The results are closely related to the discontinuity of eigenvalues with respect to the boundary conditions.
QUALITATIVE THEORY OF DYNAMICAL SYSTEMS
(2023)
Article
Mathematics, Applied
Hamed Aslani, Davod Khojasteh Salkuyeh, Fatemeh Panjeh Ali Beik
Summary: A new iterative method is proposed for solving large and sparse linear systems with three-by-three block coefficient matrices with saddle point structure. The method is studied for convergence properties and its induced preconditioner is examined to accelerate the convergence speed of GMRES method. Numerical experiments demonstrate the effectiveness of the proposed preconditioner.
Article
Operations Research & Management Science
Meilan Zeng
Summary: This paper investigates tensor Z-eigenvalue complementarity problems and proposes a semidefinite relaxation algorithm to solve the complementarity Z-eigenvalues of tensors. The algorithm shows asymptotic and finite convergence for tensors with finitely many complementarity Z-eigenvalues, and numerical experiments demonstrate the efficiency of the proposed method.
COMPUTATIONAL OPTIMIZATION AND APPLICATIONS
(2021)
Article
Mathematics
Teng Wang, Mei Feng, Xiang Wang, Hongjia Chen
Summary: In this paper, the authors investigate the relationship between Rayleigh-Ritz projection and linearization and establish bounds for the backward errors of approximate eigenpairs. Numerical experiments are conducted to support the predictions of the backward error analysis.
LINEAR & MULTILINEAR ALGEBRA
(2022)
Article
Engineering, Multidisciplinary
Harendra Singh, Rajesh K. Pandey, Devendra Kumar
Summary: The study introduces a numerical approach for studying fractional optimal control problems, converting FOCPs into a system of nonlinear algebraic equations to simplify the problem. The accuracy and applicability of the proposed method are demonstrated through convergence analysis and illustrative examples. The numerical results obtained by the method are compared with other techniques, showing its effectiveness.
INTERNATIONAL JOURNAL OF NONLINEAR SCIENCES AND NUMERICAL SIMULATION
(2021)
Article
Mathematics, Applied
Stefan Kindermann
Summary: This paper proves that Nesterov acceleration is an optimal-order iterative regularization method for linear ill-posed problems when a parameter is chosen based on the smoothness of the solution. This method works for both a priori stopping rule and discrepancy principle under Holder source conditions. The key tool to achieve these results is a representation of the residual polynomials using Gegenbauer polynomials.
Article
Mathematics, Applied
M. A. Hernandez-Veron, N. Romero
Summary: In this paper, an efficient iterative scheme is used to solve a nonsymmetric algebraic Riccati matrix equation, improving the efficiency and accuracy of Newton's method. The paper also proves a local convergence result and applies the method to a specific noisy Wiener-Hopf problem.
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS
(2022)
Article
Computer Science, Interdisciplinary Applications
Yeon-Ho Jeong, Seung-Hwan Boo, Solomon C. Yim
Summary: In this manuscript, a new effective method for eigenpair reanalysis of large-scale finite element (FE) models is proposed. This method utilizes the matrix block-partitioning algorithm in the Rayleigh-Ritz approach and expresses the Ritz basis matrix using thousands of block matrices of very small size. A new formulation is derived to avoid significant computational costs from the projection procedure. An algorithm is presented to recognize which blocks are changed in the modified FE model to achieve computational cost savings when computing new eigenpairs. The performance of the proposed method is demonstrated by solving several practical engineering problems and comparing the results with other methods.
JOURNAL OF COMPUTATIONAL DESIGN AND ENGINEERING
(2023)
Article
Mathematics, Applied
J. A. Ezquerro, M. A. Hernandez-Veron, A. A. Magrenan
Summary: We establish a global convergence result for an efficient third-order iterative process based on Chebyshev's method. By approximating the second derivative of the involved operator and using auxiliary points, we provide restricted domains of global convergence and locate the convergence regions of solutions. Numerical examples, including a Chandrashekar's integral equation problem, are used to illustrate the study.
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS
(2022)
Article
Mathematics, Applied
Andy Wathen
Summary: In this article, we discuss the importance of numerical linear algebra in computational methods for partial differential equations, specifically in solving symmetric and non-symmetric systems of equations. We also explore the approach of handling non-symmetric all-at-once systems that arise in the approximation of time-dependent problems, and suggest a method involving preconditioning with time-periodic problems.
COMPUTERS & MATHEMATICS WITH APPLICATIONS
(2022)
Article
Engineering, Electrical & Electronic
Davis Gilton, Gregory Ongie, Rebecca Willett
Summary: This paper presents an alternative approach utilizing an infinite number of iterations, which consistently improves reconstruction accuracy beyond state-of-the-art alternatives; additionally, the computational budget can be chosen at test time to optimize context-dependent trade-offs between accuracy and computation.
IEEE TRANSACTIONS ON COMPUTATIONAL IMAGING
(2021)
Article
Mathematics, Applied
Xiao-Ping Chen, Wei Wei, Xiao-Ming Pan
Summary: This paper presents the convergence factor of the successive quadratic approximation method for solving nonlinear eigenvalue problems and proposes inexact versions for reducing computational cost. The effectiveness of these modified methods is demonstrated through numerical results and analysis of their convergence properties.
APPLIED NUMERICAL MATHEMATICS
(2021)
Article
Mathematics, Applied
Kensuke Aishima
NUMERISCHE MATHEMATIK
(2015)
Article
Mathematics, Applied
Takeshi Ogita, Kensuke Aishima
JAPAN JOURNAL OF INDUSTRIAL AND APPLIED MATHEMATICS
(2018)
Article
Mathematics, Applied
Kensuke Aishima
LINEAR ALGEBRA AND ITS APPLICATIONS
(2018)
Article
Mathematics, Applied
Kensuke Aishima
LINEAR ALGEBRA AND ITS APPLICATIONS
(2018)
Article
Mathematics, Applied
Takeshi Ogita, Kensuke Aishima
JAPAN JOURNAL OF INDUSTRIAL AND APPLIED MATHEMATICS
(2019)
Article
Mathematics, Applied
Takeshi Ogita, Kensuke Aishima
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS
(2020)
Article
Mathematics, Applied
Kensuke Aishima
JAPAN JOURNAL OF INDUSTRIAL AND APPLIED MATHEMATICS
(2020)
Article
Mathematics, Applied
Kensuke Aishima
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS
(2020)
Article
Mathematics, Applied
Kensuke Aishima
Summary: Dynamic mode decomposition (DMD) is an efficient analysis method for time series data. This study introduces an adaptive averaging technique to DMD for strong convergence in the statistical sense under a newly constructed noise model. The averaging technique can be generally applied to the new noise model as a preconditioning step, and it is proven that the estimator of the original DMD is inconsistent in the statistical sense.
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS
(2023)
Article
Mathematics, Applied
Kensuke Aishima
Summary: This paper focuses on the statistical consistency analysis of the total least squares DMD (TLS-DMD) method, which is known for its robustness in handling random noise in time series data. By providing a statistical model and a general framework for designing projection methods based on efficient dimensionality reduction, the strong consistency of the estimation is proven.
JAPAN JOURNAL OF INDUSTRIAL AND APPLIED MATHEMATICS
(2023)
Article
Mathematics, Applied
Kensuke Aishima
Summary: This paper constructs a natural errors-in-variables regression model with linear equations constraints and proves the strong consistency of the estimation for the total least squares (TLS) problem. The presented asymptotic theory in the statistical sense is a generalization of the consistency analysis using ordinary total least squares for basic errors-in-variables regression models.
Article
Mathematics, Interdisciplinary Applications
Kensuke Aishima
IEICE NONLINEAR THEORY AND ITS APPLICATIONS
(2020)
Article
Mathematics, Applied
Kensuke Aishima
Article
Mathematics, Applied
Yushi Morijiri, Kensuke Aishima, Takayasu Matsuo
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)