Related papers: Formula for Hermite multivariate interpolation and…
We investigate the possibilities to calculate vector partition functions by means of iterated partial fraction decomposition, as suggested by Beck (2004). Particularly, for an important type of families of rational functions, we describe an…
A new recursive procedure for calculation of restricted partition function is suggested. An explicit formula for the restricted partition function is found based on this procedure.
We present previous results on the general solution of the multidimensional Hamilton-Jacobi equation $\frac{\partial u}{\partial t} - \frac{\partial u}{\partial x_a} \frac{\partial u}{\partial x_a}= 0$ and methods that were used to find…
This work provides a complete characterization of the solutions of a linear interpolation problem for vector polynomials. The interpolation problem consists in finding n scalar polynomials such that an equation involving a linear…
We consider Hadamard fractional derivatives and integrals of variable fractional order. A new type of fractional operator, which we call the Hadamard-Marchaud fractional derivative, is also considered. The objective is to represent these…
In the present work, an attempted was made to develop a numerical algorithm by the use of new orthogonal hybrid functions formed from hybrid of piecewise constant orthogonal sample-and-hold functions and piecewise linear orthogonal…
This note presents the multivariate Hermite criterion: a practical and powerful algorithm for determining the number of distinct real and complex roots of a zero-dimensional system of polynomials in any finite number of variables. The final…
Multiperforated plates exhibit high gradients and a loss of regularity concentrated in a boundary layer for which a direct numerical simulation becomes very expensive. For elliptic equations the solution at some distance of the boundary is…
An algorithm for generating interpolants for formulas which are conjunctions of quadratic polynomial inequalities (both strict and nonstrict) is proposed. The algorithm is based on a key observation that quadratic polynomial inequalities…
Nowadays, fractional differential equations are a well established tool to model phenomena from the real world. Since the analytical solution is rarely available, there is a great effort in constructing efficient numerical methods for their…
The main goal of this article is to present several quadratic refinements and reverses of the well known Heinz inequality, for numbers and matrices, where the refining term is a quadratic function in the mean parameters. The proposed idea…
We investigate the problem of approximating the matrix function $f(A)$ by $r(A)$, with $f$ a Markov function, $r$ a rational interpolant of $f$, and $A$ a symmetric Toeplitz matrix. In a first step, we obtain a new upper bound for the…
Through introducing a new iterative formula for divided differnce using Neville's and Aitken's algorithms,we study new iterative methods for interpolation,numerical differentiation and numerical integration formulas with arbitrary order of…
We study the partially asymmetric exclusion process with open boundaries. We generalise the matrix approach previously used to solve the special case of total asymmetry and derive exact expressions for the partition sum and currents valid…
In this paper, we propose a decomposition approach for eigenvalue problems with spatial symmetries, including the formulation, discretization as well as implementation. This approach can handle eigenvalue problems with either Abelian or…
We present efficient methods to interpolate data with a quantum computer that complement uploading techniques and quantum post-processing. The quantum algorithms are supported by the efficient Quantum Fourier Transform (QFT) and classical…
In this note we mainly study the fine Jordan-Chevalley decomposition: a refinement of the classical Jordan-Chevalley decomposition of a matrix and we pay a particular attention to the field of the coefficients of the matrix. Moreover we…
We develop a unifying framework for interpolatory $\mathcal{L}_2$-optimal reduced-order modeling for a wide classes of problems ranging from stationary models to parametric dynamical systems. We first show that the framework naturally…
We prove a complex formulation of the real interpolation method, showing that the real and complex interpolation methods are not inherently real or complex. Using this complex formulation, we prove Stein interpolation for the real…
We compute minimal bases of solutions for a general interpolation problem, which encompasses Hermite-Pad\'e approximation and constrained multivariate interpolation, and has applications in coding theory and security. This problem asks to…