Related papers: On the Jacobi formula for Bivariate Pade Approxima…

The task of approximating a function of d variables from its evaluations at a given number of points is ubiquitous in numerical analysis and engineering applications. When d is large, this task is challenged by the so-called curse of…

This paper explores the problem of analytically approximating the orbital state for a subset of orbits in a rotating potential with oblateness and ellipticity perturbations. This is done by isolating approximate differential equations for…

The Reeb space is a fundamental data structure in computational topology that represents the fiber topology of a multi-field (or multiple scalar fields), extending the level set topology of a scalar field. Efficient algorithms have been…

The computation of the entries of Jacobi operators associated with orthogonal polynomials has important applications in numerical analysis. From truncating the operator to form a Jacobi matrix, one can apply the Golub--Welsh algorithm to…

In this study, the Riccati equation is resolved using the generalized recursive integrating factor method. By applying a non-linear transformation to the dependent variable $y(x)$ of the Riccati equation, a second-order linear differential…

Shape-constrained convex regression problem deals with fitting a convex function to the observed data, where additional constraints are imposed, such as component-wise monotonicity and uniform Lipschitz continuity. This paper provides a…

We consider a proximal operator given by a quadratic function subject to bound constraints and give an optimization algorithm using the alternating direction method of multipliers (ADMM). The algorithm is particularly efficient to solve a…

This paper is concerned with the analysis and implementation of robust finite element approximation methods for mixed formulations of linear elasticity problems where the elastic solid is almost incompressible. Several novel a posteriori…

Convergence of diagonal Pad\'e approximants is studied for a class of functions which admit the integral representation $ {\mathfrak F}(\lambda)=r_1(\lambda)\int_{-1}^1\frac{td\sigma(t)}{t-\lambda}+r_2(\lambda), $ where $\sigma$ is a finite…

In this article we consider the approximation of a variable coefficient (two-sided) fractional diffusion equation (FDE), having unknown $u$. By introducing an intermediate unknown, $q$, the variable coefficient FDE is rewritten as a lower…

In this paper, we propose a two-level block preconditioned Jacobi-Davidson (BPJD) method for efficiently solving discrete eigenvalue problems resulting from finite element approximations of $2m$th ($m = 1, 2$) order symmetric elliptic…

We consider the application of implicit and linearly implicit (Rosenbrock-type) peer methods to matrix-valued ordinary differential equations. In particular the differential Riccati equation (DRE) is investigated. For the Rosenbrock-type…

It is proved that the members of the Riccati hierarchy, the so-called Riccati chain equations, can be considered as particular cases of projective Riccati equations, which greatly simplifies the study of the Riccati hierarchy. This also…

In this paper, we propose a new and simple approach to the approximation algorithms that are modified and improved from our published results. The computational and graphical examples are presented with the aid of Maple procedures.

We develop a unified method to study spectral determinants for several different manifolds, including spheres and hemispheres, and projective spaces. This is a direct consequence of an approach based on deriving recursion relations for the…

We present a recursive algorithm for multi-coefficient inversion in nonlinear Helmholtz equations with polynomial-type nonlinearities, utilizing the linearized Dirichlet-to-Neumann map as measurement data. To achieve effective recursive…

We study the bit complexity of two methods, related to the Euclidean algorithm, for computing cubic and quartic analogs of the Jacobi symbol. The main bottleneck in such procedures is computation of a quotient for long division. We give…

This paper provides an efficient recursive approach of the spectral Tau method to approximate the solution of system of generalized Abel-Volterra integral equations. In this regards, we first investigate the existence, uniqueness as well as…

Jaccard Similarity is a very common proximity measurement used to compute the similarity between two asymmetric binary vectors. Jaccard Similarity is the ratio between the 1s (Intersection of two vectors) to 1s (Union of two vectors). This…

In this paper, we present a new iterative approximate method of solving boundary value problems. The idea is to compute approximate polynomial solutions in the Bernstein form using least squares approximation combined with some properties…