9789401048965 - Error Inequalities in Polynomial Interpolation and Their Applications (Mathematics and Its Applications, Band 262) von Agarwal, R.P.; Wong, Patricia J.Y. (3 Ergebnisse)

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Taschenbuch. Zustand: Neu. Error Inequalities in Polynomial Interpolation and Their Applications | R. P. Agarwal (u. a.) | Taschenbuch | x | Englisch | 2013 | Springer | EAN 9789401048965 | Verantwortliche Person für die EU: Springer Verlag GmbH, Tiergartenstr. 17, 69121 Heidelberg, juergen[dot]hartmann[at]springer[dot]com | Anbieter: preigu.

Taschenbuch. Zustand: Neu. Druck auf Anfrage Neuware - Printed after ordering - 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 k 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.