Error Inequalities in Polynomial Interpolation and Their Applications (Paperback, Softcover reprint of the original 1st ed. 1993)

Given a function x(t) E c{n) [a, bj, points a = al < a2 < ...< ar = b and subsets aj of {0,1,"',n -1} with L:j=lcard(aj) = n, the classical interpolation problem is to find a polynomial P - (t) of degree at most (n - 1) n l such that P~~l(aj) = x{i)(aj) for i E aj, j = 1,2," r. In the first four chapters of this monograph we shall consider respectively the cases: the Lidstone interpolation (a = 0, b = 1, n = 2m, r = 2, al = a2 = {a, 2", 2m - 2}), the Hermite interpolation (aj = {a, 1,' ", kj - I}), the Abel - Gontscharoff interpolation (r = n, ai ~ ai+l, aj = {j - I}), and the several particular cases of the Birkhoff interpolation. For each of these problems we shall offer: (1) explicit representations of the interpolating polynomial; (2) explicit representations of the associated error function e(t) = x(t) - Pn-l(t); and (3) explicit optimal/sharp constants Cn,k so that the inequalities k I e{k)(t) I < C k(b -at- max I x{n)(t) I, 0 n - 1 n -, a$t$b - are satisfied. In addition, for the Hermite interpolation we shall provide explicit opti- mal/sharp constants C(n,p, v) so that the inequality II e(t) lip:::; C(n,p, v) II x{n)(t) 1111, p, v ~ 1 holds.

General

Imprint:	Springer
Country of origin:	Netherlands
Series:	Mathematics and Its Applications, 262
Release date:	October 2012
First published:	1993
Authors:	R.P. Agarwal • Patricia J.Y. Wong
Dimensions:	240 x 160 x 20mm (L x W x T)
Format:	Paperback
Pages:	366
Edition:	Softcover reprint of the original 1st ed. 1993
ISBN-13:	978-9401048965
Categories:	Books > Science & Mathematics > Mathematics > Numerical analysis Books > Science & Mathematics > Mathematics > Calculus & mathematical analysis > Differential equations Books > Science & Mathematics > Mathematics > Applied mathematics > General Promotions
LSN:	9401048967
Barcode:	9789401048965

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