Can I read Padé-Type Approximation and General Orthogonal Polynomials on EtoBox?

Padé-Type Approximation and General Orthogonal Polynomials by Claude Brezinski (auth.) is a nonfiction available to read on EtoBox.

What is Padé-Type Approximation and General Orthogonal Polynomials about?

Pade-type approximants can be applied to the approximation of the limit S of a sequence {Sn}. Let us consider the series / defined by Ci = Si+l-Si for i = 0,1, .... Then S = So+/(l). Here f(l) can be replaced by (k -l/k)f(l) and we obtain an approximate value of S given by So+ w(l)/v(l) = (boSo+ ... +bkSk)/(bo+ ... +~). This approximation depends on k since for each value of k a new polynomial v has to be chosen. This approximation can be called Vk and written as From Theorem 1.2 we get S-Vk=c(v(X»). ## 1-x If, for each k, the polynomial v does not depend on the coefficients C i then this transformation is linear and is called a summation method. The sequence {V n } converges to the same limit as the sequence {s,,} for any converging sequence {s,,} if the three conditions of Toeplitz theorem are satisfied. We shall return to this problem in the next section. ## Convergence theorems Let us now study the convergence of (n + k/k>t(t) when n~oo or k~oo. Let n Sn = I c/ and v(x) = bo + blx + ... + bkxk. Then, from the definition of w, i~O will give us ao, ... , ak-l under the necessary and sufficient condition that the following Hankel determinant be different from zero Co Cl' .• Ck-l H

Who reads Padé-Type Approximation and General Orthogonal Polynomials?

Author

Claude Brezinski (auth.)

Publisher

Birkhäuser Basel

Published

1980

Language

DE

ISBN

9783034865586

Category

nonfiction

Subjects

Social Science, Sociology, Science