Related papers: Prescription for choosing an interpolating functio…
Factorization of polynomials arises in numerous areas in symbolic computation. It is an important capability in many symbolic and algebraic computation. There are two type of factorization of polynomials. One is convention polynomial…
The suitable basis functions for approximating periodic function are periodic, trigonometric functions. When the function is not periodic, a viable alternative is to consider polynomials as basis functions. In this paper we will point out…
There is proposed a method for improving the convergence of Fourier series by function systems, orthogonal at the segment, the application of which allows for smooth functions to receive uniformly convergent series. There is also proposed…
We consider the problem of uniform interpolation of functions with values in a complex inner product space of finite dimension. This problem can be casted within a modified weighted pluripotential theoretic framework. Indeed, in the…
Kernel based regularized interpolation is a well known technique to approximate a continuous multivariate function using a set of scattered data points and the corresponding function evaluations, or data values. This method has some…
To infer a function value on a specific point $x$, it is essential to assign higher weights to the points closer to $x$, which is called local polynomial / multivariable regression. In many practical cases, a limited sample size may ruin…
We consider quadrature formulas based on interpolation using the basis functions $1/(1+t_kx)$ $(k=1,2,3,\ldots)$ on $[-1,1]$, where $t_k$ are parameters on the interval $(-1,1)$. We investigate two types of quadratures: quadrature formulas…
This article revisits the fundamental problem of parameter selection for Gaussian process interpolation. By choosing the mean and the covariance functions of a Gaussian process within parametric families, the user obtains a family of…
A selection of algorithms for the rational approximation of matrix-valued functions are discussed, including variants of the interpolatory AAA method, the RKFIT method based on approximate least squares fitting, vector fitting, and a method…
Matrices resulting from the discretization of a kernel function, e.g., in the context of integral equations or sampling probability distributions, can frequently be approximated by interpolation. In order to improve the efficiency, a…
We determine the Rolle function in Lagrange polynomial approximation using a suitable differential equation. We then propose a device for improving the Lagrange approximation by exploiting our knowledge of the Rolle function.
In this present paper, I propose a derivation of unified interpolation and extrapolation function that predicts new values inside and outside the given range by expanding direct Taylor series on the middle point of given data set.…
This work aims to introduce the framework of polynomial optimization theory to solve fractional polynomial problems (FPPs). Unlike other widely used optimization frameworks, the proposed one applies to a larger class of FPPs, not…
This paper deals with approximation of smooth convex functions $f$ on an interval by convex algebraic polynomials which interpolate $f$ at the endpoints of this interval. We call such estimates "interpolatory". One important corollary of…
A prescription is presented for the interpolation between multi-dimensional distribution templates based on one or multiple model parameters. The technique uses a linear combination of templates, each created using fixed values of the…
The versatility of data-driven approximation by interpolatory methods, originally settled for model approximation purpose, is illustrated in the context of linear controller design and stability analysis of irrational models. To this aim,…
The calculation and manipulation of large multi-variable rational functions is a key bottleneck in multi-loop calculations. In these conference proceedings, based on my article [Chawdhry (2023) arXiv:2312.03672], I present a technique to…
The standard practice of query performance prediction (QPP) evaluation is to measure a set-level correlation between the estimated retrieval qualities and the true ones. However, neither this correlation-based evaluation measure quantifies…
We study approximation by arbitrary linear combinations of $n$ translates of a single function of periodic functions. We construct some methods of this approximation for functions in a class induced by the convolution with a given function,…
We present a novel projection-based model reduction framework for parametric linear time-invariant systems that allows interpolating the transfer function at a given frequency point along parameter-dependent curves as opposed to the…