In this paper, we consider a rational algorithm for modification of a positive measure by quadratic factor, dσ̂ (t) = (t − z)2 dσ(t), where it is allowed z to be in supp(dσ).Also, we present an application of modified algorithm to the measures dσ̂ (t) = T 2 2 (t) dσ(t) and dσ ′(t) = t2T 2 2 (t) dσ(t), where T2(t) = t2 − 1 2 is the second degree monic Chebyshev polynomial of the first kind and dσ(...

Best Chebyshev approximation of real-valued data is treated by approximations obtained from solutions of parameter dependent initial value problems in ordinary diierential equations, in which the initial conditions are speciied. The problem is a modiied form of the problem treated by the authors in 9], 10], and 11]. The xing of the initial condition at t = a requires that approximation be carri...

We implement the minimax approximation for the decomposition of energy denominators in Laplace-transformed Moller-Plesset perturbation theories. The best approximation is defined by minimizing the Chebyshev norm of the quadrature error. The application to the Laplace-transformed second order perturbation theory clearly shows that the present method is much more accurate than other numerical qua...

We examine the merits of using prolate spheroidal wave functions (PSWFs) as basis functions when solving hyperbolic PDEs using pseudospectral methods. The relevant approximation theory is reviewed and some new approximation results in Sobolev spaces are established. An optimal choice of the band-limit parameter for PSWFs is derived for single-mode functions. Our conclusion is that one might gai...

Let T be a compact Hausdorff topological space and let M denote an n–dimensional subspace of the space C(T ), the space of real–valued continuous functions on T and let the space be equipped with the uniform norm. Zukhovitskii [7] attributes the Basic Theorem to E.Ya.Remez and gives a proof by duality. He also gives a proof due to Shnirel’man, which uses Helly’s Theorem, now the paper obtains a...