Article
Mathematics, Applied
Maximilian Bernkopf, Jens Markus Melenk
Summary: This paper analyzes a divergence based first order system least squares method applied to a second order elliptic model problem with homogeneous boundary conditions. Optimal convergence in the L-2(omega) norm for the scalar variable is proven. Numerical results confirm the findings.
ESAIM-MATHEMATICAL MODELLING AND NUMERICAL ANALYSIS
(2023)
Article
Mathematics, Applied
Shun Zhang
Summary: In this paper, a simple proof of the coerciveness of first-order system least-squares methods for general (possibly indefinite) second-order linear elliptic PDEs under a minimal uniqueness assumption is presented. The proof is inspired by Ku's proof [36] based on the a priori estimate of the PDE. The proof is a straightforward and short proof using the inf-sup stability of the standard variational formulation, and can potentially be applied to other equations or settings.
COMPUTERS & MATHEMATICS WITH APPLICATIONS
(2023)
Article
Biochemical Research Methods
Ruoyu Tang, Xinyu He, Ruiqi Wang
Summary: The study presents a general computational method for constructing maps between different cell fates and parametric conditions by systematic perturbations. The method does not require accurate parameter measurements or bifurcations. The maps obtained can help in understanding how systematic perturbations drive cell fate decisions and transitions, providing valuable information for predicting and controlling cell states.
Article
Mathematics, Applied
Baasansuren Jadamba, Akhtar A. Khan, Fabio Raciti, Miguel Sama
Summary: This paper develops a stochastic approximation approach for estimating the flexural rigidity within the framework of variational inequalities. The nonlinear inverse problem is analyzed as a stochastic optimization problem using an energy least-squares formulation. A stochastic variational inequality is solved by a stochastic auxiliary problem principle-based iterative scheme, which satisfies the necessary and sufficient optimality condition for the optimization problem. The convergence analysis for the proposed iterative scheme is given under general conditions on the random noise. Detailed computational results demonstrate the feasibility and efficacy of the proposed methodology.
COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION
(2022)
Article
Mathematics, Applied
Leiya Chang, Xiufang Liu, Dehui Wang, Yingchuan Jing, Chenlong Li
Summary: This paper develops a first-order random coefficient mixed-thinning integer-valued autoregressive time series model (RCMTINAR(1)) to handle data related to the counting of elements with variable character. The moments and autocovariance functions for this model are explored in the presence of an unknown innovation sequence distribution. The model parameters are estimated using conditional least squares and modified quasi-likelihood, and the asymptotic properties of the estimators are established. The performance of the estimators is investigated and compared with false modified quasi-likelihood through simulations. Additionally, the practical relevance of the model is illustrated with two applications to specific datasets, along with a comparison to existing models in the literature.
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS
(2022)
Article
Engineering, Multidisciplinary
Baolei Wei
Summary: Parameter estimation is a crucial step in grey system models for time series modeling and forecasting. This study presents a separable grey system model that encompasses both linear and nonlinear models with separable structural parameters. Three least squares-based strategies are proposed for estimating structural parameters and initial conditions. Nonlinear least squares outperforms the other two strategies, especially in scenarios with large time intervals and high noise levels. Real-world applications demonstrate the effectiveness of the proposed method in forecasting failure times of products and traffic flows.
APPLIED MATHEMATICAL MODELLING
(2023)
Article
Mathematics, Applied
Fleurianne Bertrand, Daniele Boffi
Summary: This paper discusses the spectral properties of operators associated with the least-squares finite-element approximation of elliptic partial differential equations. The convergence of discrete eigenvalues and eigenfunctions towards the corresponding continuous eigenmodes is studied and analyzed using appropriate L-2 error estimates. Both a priori and a posteriori estimates are proven.
IMA JOURNAL OF NUMERICAL ANALYSIS
(2022)
Article
Mathematics
Zaineb Yakoub, Omar Naifar, Dmitriy Ivanov
Summary: This paper presents a method to identify continuous-time fractional order systems with unknown time-delay using the bias compensated least squares algorithm. The suggested approach makes a significant contribution by estimating the system coefficients, orders, and time-delay iteratively through a nonlinear optimization algorithm. The method provides a simple and powerful algorithm with good accuracy.
Article
Forestry
Soheil Palizi, Vahab Toufigh
Summary: This study proposes three empirical models using gene expression programming (GEP) to predict the bond strength between timber and fiber-reinforced polymer (FRP) under various environmental conditions. The models consider the strength reduction in different environments and are trained and validated using data from previous studies.
EUROPEAN JOURNAL OF WOOD AND WOOD PRODUCTS
(2022)
Article
Automation & Control Systems
Soumaya Marzougui, Asma Atitallah, Saida Bedoui, Kamel Abderrahim
Summary: This paper addresses the difficulty of identifying parameters for a fractional-order Hammerstein system with white noise by developing an algorithm and studying the convergence of the identified parameters. The proposed algorithm's performance is tested through two numerical examples.
INTERNATIONAL JOURNAL OF SYSTEMS SCIENCE
(2021)
Article
Mathematics, Applied
Thomas Fuhrer, Juha Videman
Summary: We propose and analyze a least-squares finite element method for a scaled Brinkman model of fluid flow through porous media. By introducing a pseudostress variable, the pressure variable can be eliminated from the system and recovered through a simple post-processing technique. We show that the least-squares functional is uniformly equivalent to a parameter dependent norm, which implies that it can serve as an efficient and reliable a posteriori error estimator. Numerical experiments are presented to validate the proposed method.
ESAIM-MATHEMATICAL MODELLING AND NUMERICAL ANALYSIS
(2023)
Article
Engineering, Electrical & Electronic
Xiaorong Xu, Weiwei Zhu, Shuo Yang, Jianrong Bao, Wei-Ping Zhu, Zhaoting Liu
Summary: This article investigates cascaded channel estimation in intelligent reflecting surface (IRS)-assisted simultaneous wireless information and power transfer (SWIPT) system, using compressed sensing method to solve the sparse signal reconstruction problem, and proposes two cascaded channel estimation approaches. Simulation results show that these approaches have good performance in channel estimation and beamforming.
IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY
(2023)
Article
Computer Science, Interdisciplinary Applications
Mostafa Abbaszadeh, Mehdi Dehghan
Summary: The main purpose of this investigation is to develop an interpolating meshless numerical procedure for solving the stochastic parabolic interface problems. The PDE is discretized using the ISMLS approximation and reduced to a system of nonlinear ODEs. A fourth-order time discrete scheme known as ETDRK4 is used to achieve high-order numerical accuracy. Several examples with adequate complexity are examined to validate the new numerical procedure.
ENGINEERING WITH COMPUTERS
(2022)
Article
Mathematics, Applied
Minqiang Xu, Lufang Zhang, Emran Tohidi
Summary: This paper focuses on developing a fourth-order numerical scheme for one-dimensional elliptic interface problems using broken cubic spline spaces and the reproducing kernel function of W-2(1). The proposed method is proven to be stable and capable of extending to higher order schemes. Optimal convergence orders under H-2, H-1, and L-2 norms are discussed, and theoretical findings are verified by numerical experiments. Comparisons with other methods are also provided.
APPLIED NUMERICAL MATHEMATICS
(2021)
Article
Geochemistry & Geophysics
Yingming Qu, Chongpeng Huang, Chang Liu, Zhenchun Li
Summary: This study focuses on the impact and compensation techniques of multiples in deep-marine environments, proposing a method for joint primaries and multiples inversion imaging. By using curvilinear grids to match the seabed structure, the proposed method achieved clear imaging structures and high SNR in numerical examples and real data tests. The total computational cost was shown to be the least among four conventional methods.
IEEE TRANSACTIONS ON GEOSCIENCE AND REMOTE SENSING
(2021)
