相关论文: Prony's method in several variables: symbolic solu…
Multiple imputation is a straightforward method for handling missing data in a principled fashion. This paper presents an overview of multiple imputation, including important theoretical results and their practical implications for…
According to Lidstone interpolation theory, an entire function of exponential type $<\pi$ is determined by it derivatives of even order at $0$ and $1$. This theory can be generalized to several variables. Here we survey the theory for a…
A general formula is presented for any order derivative of Chebyshev polynomials instead of the existing recursive relationship. Hence, the Chebyshev finite difference method is made applicable not only to second order problems but also to…
The goal of this paper is to provide computational tools able to find a solution of a system of polynomial inequalities. The set of inequalities is reformulated as a system of polynomial equations. Three different methods, two of which…
In this survey we describe some modifications of Prony's method. In particular, we consider the recovery of general expansions into eigenfunctions of linear differential operators of first order and show, how these expansions can be…
Neville's algorithm is known to provide an efficient and numerically stable solution for polynomial interpolations. In this paper, an extension of this algorithm is presented which includes the derivatives of the interpolating polynomial.
The generic chaining method provides a sharp description of the suprema of many random processes in terms of the geometry of their index sets. The chaining functionals that arise in this theory are however notoriously difficult to control…
For Paley-Wiener functions on weighted combinatorial finite or infinite graphs we develop a weighted sampling theory in which samples are defined as inner products with weight functions (measuring devices). Three reconstruction methods are…
Model based signal processing or signal analysis or signal representation has a rather different point of view from the more traditional filtering and algorithm based approaches. However, in all of these, the names of Prony, Pad\'e, and…
One way to investigate the precision of estimates likely to result from planned experiments and planned epidemiological studies is to simulate a large number of possible outcomes and analyse the sets of possible results. This appears to be…
We introduce a new method to price American options based on Chebyshev interpolation. In each step of a dynamic programming time-stepping we approximate the value function with Chebyshev polynomials. The key advantage of this approach is…
It is well known that the Newton method may not converge when the initial guess does not belong to a specific quadratic convergence region. We propose a family of new variants of the Newton method with the potential advantage of having a…
The interaction between two particles with shape or interaction anisotropy can be modeled using a pairwise potential energy function that depends on their relative position and orientation; however, this function is often challenging to…
In this paper, we present a generic parametrization of generically zero-dimensional parametric polynomial systems. More specifically, we study the specialization properties of the Rational Univariate Representation and derive bounds on the…
We propose a new approach to the combinatorial interpretations of linearization coefficient problem of orthogonal polynomials. We first establish a difference system and then solve it combinatorially and analytically using the method of…
Synthesis problems for linkages in kinematics often yield large structured parameterized polynomial systems which generically have far fewer solutions than traditional upper bounds would suggest. This paper describes statistical models for…
Adaptive rational interpolation has been designed in the context of image processing as a new nonlinear technique that avoids the Gibbs phenomenon when we approximate a discontinuous function. In this work, we present a generalization to…
We use character polynomials to obtain a positive combinatorial interpretation of the multiplicity of the sign representation in irreducible polynomial representations of $GL_n(\mathbb{C})$ indexed by two-column and hook partitions. Our…
In this paper, we develop a method of evaluating general exponential sums with rational amplitude functions for multiple variables which complements works by T. Cochrane and Z. Zheng on the single variable case. As an application, for…
The main purpose of this paper is to construct not only generating functions of the new approach Genocchi type numbers and polynomials but also interpolation function of these numbers and polynomials which are related to a, b, c arbitrary…