Related papers: Using covariance extension equation to solve the N…
For $m,n \in \mathbb{N}$, $m\geq 1$ and a given function $f : \mathbb{R}^m\longrightarrow \mathbb{R}$ the polynomial interpolation problem (PIP) is to determine a \emph{generic node set} $P \subseteq \mathbb{R}^m$ and the coefficients of…
In the Markov and covariance interpolation problem a transfer function $W$ is sought that match the first coefficients in the expansion of $W$ around zero and the first coefficients of the Laurent expansion of the corresponding spectral…
This paper deals with the solving of variational inequality problem where the constrained set is given as the intersection of a number of fixed-point sets. To this end, we present an extrapolated sequential constraint method. At each…
The synthesis of optimization algorithms typically follows a design-first-analyze-later approach, which often obscures fundamental performance limitations and hinders the systematic design of algorithms operating at the achievable…
Constrained non-convex optimization problems frequently arise in control applications. Solving such problems is inherently challenging, as existing methods often converge to suboptimal local minima or incur prohibitive computational costs.…
In this article we study the estimation of bifurcation coefficients in nonlinear branching problems by means of Rayleigh-Ritz approximation to the eigenvectors of the corresponding linearized problem. It is essential that the approximations…
In this paper we investigate the use of Richardson extrapolation to estimate the convergence rates for numerical solutions to advection problems involving discontinuities. We use modified equation analysis to describe the expectation of the…
The Van Leer approach for the approximation of nonlinear scalar conservation laws is studied in one space dimension. The problem can be reduced to a nonlinear interpolation and we propose a convexity property for the interpolated values. We…
In this paper, we consider a broad class of nonsmooth and nonconvex fractional programs, where the numerator can be written as the sum of a continuously differentiable convex function whose gradient is Lipschitz continuous and a proper…
In this paper we obtain a noncommutative multivariable analogue of the classical Nevanlinna-Pick interpolation problem for analytic functions with positive real parts on the open unit disc. As consequences, we deduce some results concerning…
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 give a solution to Pick's interpolation problem on the unit polydisc in $\mathbb{C}^n$, $n\geq 2$, by characterizing all interpolation data that admit a $\mathbb{D}$-valued interpolant, in terms of a family of positive-definite kernels…
In this paper, we propose an inertial alternating direction method of multipliers for solving a class of non-convex multi-block optimization problems with \emph{nonlinear coupling constraints}. Distinctive features of our proposed method,…
In this work we present a method, based on the use of Bernstein polynomials, for the numerical resolution of some boundary values problems. The computations have not need of particular approximations of derivatives, such as finite…
We present new techniques for reducing a multivariate sparse polynomial to a univariate polynomial. The reduction works similarly to the classical and widely-used Kronecker substitution, except that we choose the degrees randomly based on…
Image inpainting involves filling in damaged or missing regions of an image by utilizing information from the surrounding areas. In this paper, we investigate a highly nonlinear partial differential equation inspired by the modified…
An indefinite generalization of Nudel'man's problem is used in a systematic approach to interpolation theorems for generalized Schur and Nevanlinna functions with interior and boundary data. Besides results on existence criteria for…
The extended form of the classical polynomial cubic B-spline function is used to set up a collocation method for some initial boundary value problems derived for the Korteweg-de Vries-Burgers equation. Having nonexistence of third order…
Some variants of the numerical Picard iterations method are presented to solve an IVP for an ordinary differential system. The term numerical emphasizes that a numerical solution is computed. The method consists in replacing the right hand…
In this paper we address the problem of interpolating a spline developable patch bounded by a given spline curve and the first and the last rulings of the developable surface. In order to complete the boundary of the patch a second spline…