Band 262
Error Inequalities in Polynomial Interpolation and Their Applications
Aus der Reihe
Mathematics and Its Applications
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Sprache:Englisch
Fr. 72.90
inkl. gesetzl. MwSt.,
Beschreibung
Produktdetails
Einband
Taschenbuch
Erscheinungsdatum
26.10.2012
Verlag
Springer NetherlandSeitenzahl
366
Maße (L/B/H)
24/16/2.1 cm
Auflage
Softcover reprint of the original 1st ed. 1993
Sprache
Englisch
ISBN
978-94-010-4896-5
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.
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