相关论文: Generalizing Dodgson's method: a "double-crossing"…
Conventional statistical wisdom established a well-understood relationship between model complexity and prediction error, typically presented as a U-shaped curve reflecting a transition between under- and overfitting regimes. However,…
For academics and practitioners concerned with computers, business and mathematics, one central issue is supporting decision makers. In this paper, we propose a generalization of Decision Matrix Method (DMM), using Neutrosophic logic. It…
An iteration-free method of domain decomposition is considered for approximate solving a boundary value problem for a second-order parabolic equation. A standard approach to constructing domain decomposition schemes is based on a partition…
A new approximation method for inverting the Poisson's equation is presented for a continuously distributed and finite-sized source in an unbound domain. The advantage of this image multipole method arises from its ability to place the…
A random matrix is likely to be well conditioned, and motivated by this well known property we employ random matrix multipliers to advance some fundamental matrix computations. This includes numerical stabilization of Gaussian elimination…
We present a novel deep learning approach to approximate the solution of large, sparse, symmetric, positive-definite linear systems of equations. These systems arise from many problems in applied science, e.g., in numerical methods for…
A cumbersome operation in numerical analysis and linear algebra, optimization, machine learning and engineering algorithms; is inverting large full-rank matrices which appears in various processes and applications. This has both numerical…
The concepts of differentiation and integration for matrices were introduced for studying zeros and critical points of complex polynomials. Any matrix is differentiable, however not all matrices are integrable. The purpose of this paper is…
The proposed article aims at offering a comprehensive tutorial for the computational aspects of structured matrix and tensor factorization. Unlike existing tutorials that mainly focus on {\it algorithmic procedures} for a small set of…
Combining empirical risk minimization with capacity control is a classical strategy in machine learning when trying to control the generalization gap and avoid overfitting, as the model class capacity gets larger. Yet, in modern deep…
A fundamental task in numerical computation is the solution of large linear systems. The conjugate gradient method is an iterative method which offers rapid convergence to the solution, particularly when an effective preconditioner is…
We present double pooling, a simple, easy-to-implement variation on test pooling, that in certain ranges for the a priori probability of a positive test, is significantly more efficient than the standard single pooling approach (the Dorfman…
Domain generalization algorithms use training data from multiple domains to learn models that generalize well to unseen domains. While recently proposed benchmarks demonstrate that most of the existing algorithms do not outperform simple…
The confusion matrix is a standard tool for evaluating classifiers by providing insights into class-level errors. In heterogeneous settings, its values are shaped by two main factors: class similarity -- how easily the model confuses two…
The very weak solution of the Poisson equation with $L^2$ boundary data is defined by the method of transposition. The finite element solution with regularized boundary data converges in the $L^2(\Omega)$-norm with order $1/2$ in convex…
Modern causal inference methods allow machine learning to be used to weaken parametric modeling assumptions. However, the use of machine learning may result in complications for inference. Doubly-robust cross-fit estimators have been…
The averaging method provides a powerful tool for studying evolution in near-integrable systems. Existence of separatrices in the phase space of the underlying integrable system is an obstacle for application of standard results that…
The fast assembling of stiffness and mass matrices is a key issue in isogeometric analysis, particularly if the spline degree is increased. We present two algorithms based on the idea of sum factorization, one for matrix assembling and one…
Several approaches are discussed how to understand the solution of the Dirichlet problem for the Poisson equation when the Dirichlet data are non-smooth such as if they are in $L^2$ only. For the method of transposition (sometimes called…
A mathematical analysis is established for the weak Galerkin finite element methods for the Poisson equation with Dirichlet boundary value when the curved elements are involved on the interior edges of the finite element partition or/and on…