This paper presents an efficient method for designing complex infinite impulse response digital filters in the complex Chebyshev sense. The proposed method is based on the formulation of a generalized eigenvalue problem by using the Remez multiple exchange algorithm. Hence, the filter coefficients can be easily obtained by solving the eigenvalue problem to find the absolute minimum eigenvalue, ...

Numerical methods for strongly oscillatory and singular functions are given in this paper. We present an alternative numerical solution for of oscillatory integrals of the general form Where and are smooth functions in the interval [a, b]. Also ε ω and . In order to achieve this goal and avoid singularity, the mentioned integral is solved by the modified moments using interpolating at the Cheby...

We present the K-grid, a structure for storage and retrieval of affective knowledge. The K-grid is an ubiquitous-affective computing structure that can be used to capture and disseminate affectively laden knowledge, based on activities and past experiences. The knowledge is recorded in special substructures (Knodes) which are initially linked sequentially, based on the chronological order of th...

Data interpolation is a fundamental data processing tool in scientific studies and engineering applications. However, when interpolating data points on an equidistant grid using polynomials, the so-called Runge phenomenonmay occur, making polynomial interpolation unreliable. Although there are some methods proposed to defeat the Runge phenomenon, it is still an open problem which parameter sequ...

Denote by Ln the projection operator obtained by applying the Lagrange interpolation method, weighted by (1 − x), at the zeros of the Chebyshev polynomial of the second kind of degree n + 1. The norm ‖Ln‖ = max ‖f‖∞≤1 ‖Lnf‖∞, where ‖ · ‖∞ denotes the supremum norm on [−1, 1], is known to be asymptotically the same as the minimum possible norm over all choices of interpolation nodes for unweight...

We determine the infinite sequences (ak) of integers that can be generated by polynomials with integral coefficients, in the sense that for each finite initial segment of length n there is an integral polynomial fn(x) of degree < n such that ak = fn(k) for k = 0, 1, . . . , n − 1. Let P be the set of such sequences and Π the additive group of all infinite sequences of integers. Then P is a subg...

• Asymptotics of the Lebesgue constant for Lagrange interpolation based on Lissajous-Chebyshev node points. partial sums Fourier series generated by anisotropically dilated rhombus. Formula Dirichlet kernel with frequencies in In this paper asymptotic formulas are given constants three special approximation processes related to ? 1 -partial series. particular, we consider polynomials points, rh...

We present a new parallel algorithm for the fast generation of discrete Chebyshev polynomials. By fast we mean that the time complexity of the obtained parallel algorithm is of order O(logn), where n is the degree of the (n+1)st polynomial to be generated, and the number of available processors is assumed to be equal to a polynomial order of the input size. The parallel algorithm makes extensiv...

Methods for stochastic trace estimation often require the repeated evaluation of expressions form zTpn(A)z, where A is a symmetric matrix and pn degree n polynomial written in standard or Chebyshev basis. We show how to evaluate these using only ⌈n∕2⌉ matrix–vector products, thus substantially reducing cost existing algorithms that use interpolation Taylor series.

In this paper, we consider the problem of interpolating univariate polynomials over a eld of characteristic zero that are sparse in (a) the Pochhammer basis or, (b) the Chebyshev basis. The polynomials are assumed to be given by black boxes, i.e., one can obtain the value of a polynomial at any point by querying its black box. We describe eecient new algorithms for these problems. Our algorithm...