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Although evaluation of the expectations on the Ising model is essential in various applications, it is mostly infeasible because of intractable multiple summations. Spatial Monte Carlo integration (SMCI) is a sampling-based approximation.…
Searching for numerical methods that combine facility and efficiency, while remaining accurate and versatile, is critical. Often, irregular geometries challenge traditional methods that rely on structured or body-fitted meshes. Meshless…
The method of the fundamental solutions (MFS) is used to construct an approximate solution for a partial differential equation in a bounded domain. It is demonstrated by combining the fundamental solutions shifted to the points outside the…
In this paper, we develop regularized discrete least squares collocation and finite volume methods for solving two-dimensional nonlinear time-dependent partial differential equations on irregular domains. The solution is approximated using…
The method of fundamental solution (MFS) is an efficient meshless method for solving a boundary value problem in an exterior unbounded domain. The numerical solution obtained by the MFS is accurate, while the corresponding matrix equation…
iALS is a popular algorithm for learning matrix factorization models from implicit feedback with alternating least squares. This algorithm was invented over a decade ago but still shows competitive quality compared to recent approaches like…
Partial Least Squares (PLS) is a widely used method for data integration, designed to extract latent components shared across paired high-dimensional datasets. Despite decades of practical success, a precise theoretical understanding of its…
This study presents a generalised least squares based method for fitting polygons and ellipses to data points. The method is based on a trigonometric fitness function that approximates a unit shape accurately, making it applicable to…
Neural networks have shown significant potential in solving partial differential equations (PDEs). While deep networks are capable of approximating complex functions, direct one-shot training often faces limitations in both accuracy and…
We consider the problem of approximating an unknown function from point evaluations. This problem is a crucial subproblem in many modern (nonlinear) approximation schemes. When obtaining these point evaluations is costly, minimising the…
Iteratively reweighted least square (IRLS) is a popular approach to solve sparsity-enforcing regression problems in machine learning. State of the art approaches are more efficient but typically rely on specific coordinate pruning schemes.…
In real data analysis with structural equation modeling, data are unlikely to be exactly normally distributed. If we ignore the non-normality reality, the parameter estimates, standard error estimates, and model fit statistics from normal…
This paper introduces a novel adaptive framework for processing dynamic flow signals over simplicial complexes, extending classical least-mean-squares (LMS) methods to high-order topological domains. Building on discrete Hodge theory, we…
A general stochastic algorithm for solving mixed linear and nonlinear problems was introduced in [11]. We show in this paper how it can be used to solve the fault inverse problem, where a planar fault in elastic half-space and a slip on…
Projected least squares (PLS) is an intuitive and numerically cheap technique for quantum state tomography. The method first computes the least-squares estimator (or a linear inversion estimator) and then projects the initial estimate onto…
This is a short description and basic introduction to the Integrated nested Laplace approximations (INLA) approach. INLA is a deterministic paradigm for Bayesian inference in latent Gaussian models (LGMs) introduced in Rue et al. (2009).…
The purpose of this work is to introduce a new idea of how to avoid the factorization of large matrices during the solution of stiff systems of ODEs. Starting from the general form of an explicit linear multistep method we suggest to…
This paper introduces a new method for discretizing and solving integral equation formulations of Maxwell's equations which achieves spectral accuracy for smooth surfaces. The approach is based on a hybrid Nystr\"om-collocation method using…
Multivariate cortico-muscular analysis has recently emerged as a promising approach for evaluating the corticospinal neural pathway. However, current multivariate approaches encounter challenges such as high dimensionality and limited…
In [7], a new iterative method for solving linear system of equations was presented which can be considered as a modification of the Gauss-Seidel method. Then in [4] a different approach, say 2D-DSPM, and more effective one was introduced.…