Let f(z) be analytic at the origin, and for e >0, let f(ez) be best approximated in the Chebyshev sense on the unit disk by a rational function of type (m, n). It has been shown previously by the CF method that the error curve for this approximation deviates from a circle by at most O(e 2m+2n+3) as e 0. We prove here that this bound is sharp in two senses: the error curve for a given function c...

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 approximations of the graph multipliers by shifted Chebyshev polynomials, whose recurrence relations make them readily amenable to distributed computation. We...

In a recent paper we showed that er ror curves in po lynomia l Chebyshev a p p r o x i m a t i o n of ana ly t ic functions on the unit disk tend to a p p r o x i m a t e perfect circles abou t the origin [23]. M a k i n g use of a theorem of Ca ra th6odo ry and Fej6r, we der ived in the process a me thod for calculat ing near-bes t a p p r o x i m a t i o n s rapid ly by finding the pr incipal...

The ECG (Electrocardiogram) signal represents electrical activity of heart and is recorded for monitoring and diagnostic purpose. These signals are corrupted by artifacts during acquisition and transmission predominantly by high frequency noise due to power line interference, electrode movements, etc. Addition of these noise change the amplitude and shape of the ECG signal which affect accurate...

and Applied Analysis 3 where we refer to 1.4 for the am’s and we follow the convention ∏m−1 j m · · · 1. We can easily check that cm’s satisfy the following relation: m 2 m 1 cm 2 − ( m2 − n2 ) cm am 2.2 for any m ∈ {0, 1, 2, . . .}. Theorem 2.1. Assume that n is a positive integer and the radius of convergence of the power series ∑∞ m 0 amx m is ρ > 0. Let ρ0 min{1, ρ}. Then, every solution y ...

This paper is concerned with Chebyshev approximation by exponentials on finite subsets. We take into account that varisolvency does not hold for exponentials in general. A bound for the derivatives of exponentials is established and convergence of the solutions for the discrete problems is proved in the topology of compact convergence on the open interval.

We apply methods and techniques of tropical optimization to develop a new theoretical and computational framework for the implementation of the Analytic Hierarchy Process in multi-criteria problems of rating alternatives from pairwise comparison data. The framework involves the Chebyshev approximation of pairwise comparison matrices by consistent matrices in the logarithmic scale. We reduce the...

It is well known that a near minimax polynomial approximation p is obtained by truncating the Chebyshev series of a function fafter n + 1 terms. It is shown that if /'E C' " + " [-1, I], then 1I.f-pII may be expressed in terms off' " ' I) in the same manner as the error of minimax approximation. The result is extended to other types of near minimax approximation.

Here we are concerned with the best approximation by polynomials to rational functions in the uniform norm. We give some new theorems about the best approximation of 1/(1 + x) and 1/(x − a) where a > 1. Finally we extend this problem to that of computing the best approximation of the Chebyshev expansion in uniform norm and give some results and conjectures about this.  2005 IMACS. Published by...

When a function f(x) is holomorphic on an interval x ∈ [a, b], its roots on the interval can be computed by the following three-step procedure. First, approximate f(x) on [a, b] by a polynomial fN (x) using adaptive Chebyshev interpolation. Second, form the Chebyshev– Frobenius companion matrix whose elements are trivial functions of the Chebyshev coefficients of the interpolant fN (x). Third, ...