Related papers: Algorithms for pointwise and piecewise polynomial …
In the article we propose a general scheme for solutions of some approximation problems under a rather general setting. We illustrate the application of the proposed scheme by a series of examples, in particular we show that many results in…
We describe efficient algorithms to search for cases in which binomial coefficients are equal or almost equal, give a conjecturally complete list of all cases where two binomial coefficients differ by 1, and give some identities for…
In this work we provide a novel approach for computing the coefficients of the characteristic polynomial of a square matrix. We demonstrate that each coefficient can be efficiently represented by a set of circle graphs. Thus, one can employ…
We give a new procedure in Maple for finding the k-th power of a martix. The algorithm is based on the article [1].
In this paper, we construct an algorithm for minimising piecewise smooth functions for which derivative information is not available. The algorithm constructs a pair of quadratic functions, one on each side of the point with smallest known…
We develop fixed-point algorithms for the approximation of structured matrices with rank penalties. In particular we use these fixed-point algorithms for making approximations by sums of exponentials, or frequency estimation. For the basic…
Computation of (approximate) polynomials common factors is an important problem in several fields of science, like control theory and signal processing. While the problem has been widely studied for scalar polynomials, the scientific…
Sparse polynomial approximation has become indispensable for approximating smooth, high- or infinite-dimensional functions from limited samples. This is a key task in computational science and engineering, e.g., surrogate modelling in…
In this paper we present a novel non-parametric method of simplifying piecewise linear curves and we apply this method as a statistical approximation of structure within sequential data in the plane. We consider the problem of minimizing…
Given a set of matrices, modeled as samples of a matrix-valued function, we suggest a method to approximate the underline function using a product approximation operator. This operator extends known approximation methods by exploiting the…
Finding the product of two polynomials is an essential and basic problem in computer algebra. While most previous results have focused on the worst-case complexity, we instead employ the technique of adaptive analysis to give an improvement…
Quadratically optimized polynomials are described which are useful in multi-bosonic algorithms for Monte Carlo simulations of quantum field theories with fermions. Algorithms for the computation of the coefficients and roots of these…
We suggest a new optimization technique for minimizing the sum $\sum_{i=1}^n f_i(x)$ of $n$ non-convex real functions that satisfy a property that we call piecewise log-Lipschitz. This is by forging links between techniques in computational…
We study the k-median and k-center problems in probabilistic graphs. We analyze the hardness of these problems, and propose several algorithms with improved approximation ratios compared with the existing proposals.
We propose the superiorization of incremental algorithms for tomographic image reconstruction. The resulting methods follow a better path in its way to finding the optimal solution for the maximum likelihood problem in the sense that they…
We introduce a probabilistic approach to the LMS filter. By means of an efficient approximation, this approach provides an adaptable step-size LMS algorithm together with a measure of uncertainty about the estimation. In addition, the…
An algorithm for the systematic analytical approximation of multi-scale Feynman integrals is presented. The algorithm produces algebraic expressions as functions of the kinematical parameters and mass scales appearing in the Feynman…
In this paper, we introduce a method known as polynomial frame approximation for approximating smooth, multivariate functions defined on irregular domains in $d$ dimensions, where $d$ can be arbitrary. This method is simple, and relies only…
In this work, we present a new way to compute the Taylor polynomial of the matrix exponential which reduces the number of matrix multiplications in comparison with the de-facto standard Patterson-Stockmeyer method. This reduction is…
Combining the techniques of approximation algorithms and parameterized complexity has long been considered a promising research area, but relatively few results are currently known. In this paper we study the parameterized approximability…