Related papers: Two curve Chebyshev approximation and its applicat…

Approximating adequate number of clusters in multidimensional data is an open area of research, given a level of compromise made on the quality of acceptable results. The manuscript addresses the issue by formulating a transductive…

Spectral clustering is a widely studied problem, yet its complexity is prohibitive for dynamic graphs of even modest size. We claim that it is possible to reuse information of past cluster assignments to expedite computation. Our approach…

The theory of Chebyshev approximation has been extensively studied. In most cases, the optimality conditions are based on the notion of alternance or alternating sequence (that is, maximal deviation points with alternating deviation signs).…

Unions of graph multiplier operators are an important class of linear operators for processing signals defined on graphs. We present a novel method to efficiently distribute the application of these operators. The proposed method features…

Approximation theory plays a central role in numerical analysis, undergoing continuous evolution through a spectrum of methodologies. Notably, Lebesgue, Weierstrass, Fourier, and Chebyshev approximations stand out among these methods.…

We present two new quantum algorithms for reaction-diffusion equations that employ the truncated Chebyshev polynomial approximation. This method is employed to numerically solve the ordinary differential equation emerging from the…

We address the problem of the best uniform approximation by linear combinations of a finite system of functions. If the system is Chebyshev and the problem is unconstrained, then the classical Remez algorithm provides a fast and precise…

Chebyshev interpolation polynomials exhibit the exponential approximation property to analytic functions on a cube. Based on the Chebyshev interpolation polynomial approximation, we propose iterative polynomial approximation algorithms to…

We consider the problem of clustering misaligned curves. According to our similarity measure, two curves are considered similar if they have the same shape after being aligned, and the warping function does not differ from the identity…

In this paper, we derive optimality conditions (Chebyshev approximation) for multivariate functions. The theory of Chebyshev (uniform) approximation for univariate functions is very elegant. The optimality conditions are based on the notion…

Approximation theorem is one of the most important aspects of numerical analysis that has evolved over the years with many different approaches. Some of the most popular approximation methods include the Lebesgue approximation theorem, the…

We propose a new algorithm to the problem of polygonal curve approximation based on a multiresolution approach. This algorithm is suboptimal but still maintains some optimality between successive levels of resolution using dynamic…

The theory of Chebyshev (uniform) approximation for univariate polynomial and piecewise polynomial functions has been studied for decades. The optimality conditions are based on the notion of alternating sequence. However, the extension the…

There is presented an approach to find an approximation polynomial of a function with two variables based on the two dimensional discrete Fourier transform. The approximation polynomial is expressed through Chebyshev polynomials. There is…

The constrained mock-Chebyshev least squares operator is a linear approximation operator based on an equispaced grid of points. Like other polynomial or rational approximation methods, it was recently introduced in order to defeat the Runge…

Unions of graph Fourier multipliers are an important class of linear operators for processing signals defined on graphs. We present a novel method to efficiently distribute the application of these operators to the high-dimensional signals…

In this paper we propose a new approach to least squares approximation problems. This approach is based on partitioning and Schur function. The nature of this approach is combinatorial, while most existing approaches are based on algebra…

In this paper we develop an optimisation based approach to multivariate Chebyshev approximation on a finite grid. We consider two models: multivariate polynomial approximation and multivariate generalised rational approximation. In the…

A new result in convex analysis on the calculation of proximity operators in certain scaled norms is derived. We describe efficient implementations of the proximity calculation for a useful class of functions; the implementations exploit…

We develop a computationally efficient and robust algorithm for generating pseudo-random samples from a broad class of smooth probability distributions in one and two dimensions. The algorithm is based on inverse transform sampling with a…