Related papers: Orthogonal Rational Approximation of Transfer Func…
An operator theoretic approach to orthogonal rational functions on the unit circle with poles in its exterior is presented in this paper. This approach is based on the identification of a suitable matrix representation of the multiplication…
Quantum signal processing is a powerful framework in quantum algorithms, playing a central role in Hamiltonian simulation and related applications. The sequence of polynomials implemented at each step of this protocol provides a polynomial…
The Sanathanan-Koerner iteration developed in 1963 is classical approach for rational approximation. This approach multiplies both sides of the approximation by the denominator polynomial yielding a linear problem and then introduces a…
Strictly Positive Real (SPR) transfer functions arise in many areas of engineering like passivity theory in circuit analysis and adaptive control to name a few. In many physical systems, it is possible to conclude that the system is…
We present two algorithms for constructing orthonormal bases of rational function vectors with respect to a discrete inner product, and discuss how to use them for a rational approximation problem. Building on the pencil-based formulation…
Orthogonal rational functions (ORF) on the unit circle generalize orthogonal polynomials (poles at infinity) and Laurent polynomials (poles at zero and infinity). In this paper we investigate the properties of and the relation between these…
Radial Basis Function Networks (RBFNs) are used primarily to solve curve-fitting problems and for non-linear system modeling. Several algorithms are known for the approximation of a non-linear curve from a sparse data set by means of RBFNs.…
We introduce sequences of functions orthogonal on a finite interval: proper orthogonal rational functions, orthogonal exponential functions, orthogonal logarithmic functions, and transmuted orthogonal polynomials
The purpose of this paper is to introduce a very efficient algorithm for signal extrapolation. It can widely be used in many applications in image and video communication, e. g. for concealment of block errors caused by transmission errors…
It's well know that Radial Basis Function approximants suffers of bad conditioning if the simple basis of translates is used. A recent work of M.Pazouki and R.Schaback gives a quite general way to build stable, orthonormal bases for the…
We introduce an algorithm of joint approximation of a function and its first derivative by alternative orthogonal polynomials on the interval [0,1].The algorithm exhibits properties of shape preserving approximation for the function. A weak…
In functional data analysis (FDA), covariance function is fundamental not only as a critical quantity for understanding elementary aspects of functional data but also as an indispensable ingredient for many advanced FDA methods. This paper…
This paper describes a very efficient algorithm for image signal extrapolation. It can be used for various applications in image and video communication, e.g. the concealment of data corrupted by transmission errors or prediction in video…
We propose and analyse numerical algorithms based on weighted least squares for the approximation of a real-valued function on a general bounded domain $\Omega \subset \mathbb{R}^d$. Given any $n$-dimensional approximation space $V_n…
We propose a novel class of prior distributions for sequences of orthogonal functions, which are frequently required in various statistical models such as functional principal component analysis (FPCA). Our approach constructs priors…
A rational approximation by a ratio of polynomial functions is a flexible alternative to polynomial approximation. In particular, rational functions exhibit accurate estimations to nonsmooth and non- Lipschitz functions, where polynomial…
In this paper we consider a family of algorithms for approximate implicitization of rational parametric curves and surfaces. The main approximation tool in all of the approaches is the singular value decomposition, and they are therefore…
The development of Kolmogorov-Arnold networks (KANs) marks a significant shift from traditional multi-layer perceptrons in deep learning. Initially, KANs employed B-spline curves as their primary basis function, but their inherent…
We consider linear dynamical systems of ordinary differential equations or differential algebraic equations. Physical parameters are substituted by random variables for an uncertainty quantification. We expand the state variables as well as…
Spectral representations of the dilation and translation operators on $L^2({\mathbb R})$ are built through appropriate bases. Orthonormal wavelets and multiresolution analysis are then described in terms of rigid operator-valued functions…