Related papers: Using covariance extension equation to solve the N…
The design of numerical boundary conditions is a challenging problem that has been tackled in different ways depending on the nature of the problem and the numerical scheme used to solve it. In this paper we present a new weighted…
We present a new formula for divided difference and few new schemes of divided difference tables in this paper. Through this, we derive new interpolation, numerical differentiation and numerical integration formulas with arbitrary order of…
Along this work we study an indefinite abstract smoothing problem. After establishing necessary and sufficient conditions for the existence of solutions to this problem, the set of admissible parameters is discussed in detail. Then, its…
We present a Hermite interpolation problem via splines of odd-degree which, to the best knowledge of the authors, has not been considered in the literature on interpolation via odd-degree splines. In this new interpolation problem, we…
Extrapolation is a well-known technique for solving convex optimization and variational inequalities and recently attracts some attention for non-convex optimization. Several recent works have empirically shown its success in some machine…
We give new improvements to the Chudnovsky-Chudnovsky method that provides upper bounds on the bilinear complexity of multiplication in extensions of finite fields through interpolation on algebraic curves. Our approach features three…
We consider nodal-based Lagrangian interpolations for the finite element approximation of the Maxwell eigenvalue problem. The first approach introduced is a standard Galerkin method on Powell-Sabin meshes, which has recently been shown to…
In this paper we present some open problems pertaining to the approximation theory involved in the solution of the important class of Nonlinear Partial Differential Equations (NPDEs) of integrable type. For this class of NPDEs, any Initial…
In this paper we present an estimate of accuracy for a piecewise polynomial approximation of a classical numerical solution to a non linear differential problem. We suppose the numerical solution U is computed using a grid with a small…
We investigate isometric and algebraic isomorphism problems for multiplier algebras associated with Dirichlet series kernels that possess the complete Nevanlinna-Pick (CNP) property. A central aspect of our work is the explicit…
The unique solvability and error analysis of the original Lagrange multiplier approach proposed in [8] for gradient flows is studied in this paper. We identify a necessary and sufficient condition that must be satisfied for the nonlinear…
In the space of all entire functions it is solved the problem of interpolation taking into account multiplicities by sums of the series of exponentials with the exponents from a given set. It is found a criterion of solubility of the…
In the paper we discuss the problem of uniqueness of left inverses (solutions of two point Nevanlinna-Pick problem) in bounded convex domains, strongly linearly convex domains, the symmetrized bidisc and the tetrablock.
We develop a recursive method for perturbative solutions of the Fokker-Planck equation with nonlinear drift. The series expansion of the time-dependent probability density in terms of powers of the coupling constant is obtained by solving a…
This paper demonstrates a practical method for computing the solution of an expectation-constrained robust maximization problem with immediate applications to model-free no-arbitrage bounds and super-replication values for many financial…
We revisit the image compression problem using the framework introduced by Ringh, Karlsson and Lindquist. More precisely, we explore the possibility to consider a family of objective functions and a different way to design the prior in the…
Vector extrapolation methods are widely used in large-scale simulation studies, and numerous extrapolation-based acceleration techniques have been developed to enhance the convergence of linear and nonlinear fixed-point iterative methods.…
This paper deals with maximum entropy completion of partially specified block-circulant matrices. Since positive definite symmetric circulants happen to be covariance matrices of stationary periodic processes, in particular of stationary…
A modular method was suggested before to recover a band limited signal from the sample and hold and linearly interpolated (or, in general, an nth-order-hold) version of the regular samples. In this paper a novel approach for compensating…
We show that a recent interpolative new proof of the Bohnenblust--Hille inequality, when suitably handled, recovers its best known constants. This seems to be unexpectedly surprising since the known interpolative approaches only provide…