Error Inequalities in Polynomial Interpolation and Their Applications
Published on 26. October 2012
Book
Paperback/Softback
X, 366 pages
978-94-010-4896-5 (ISBN)
Description
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.
More details
Series
Edition
Softcover reprint of the original 1st ed. 1993
Language
English
Place of publication
Dordrecht
Netherlands
Target group
Professional and scholarly
Research
Illustrations
X, 366 p.
Dimensions
Height: 240 mm
Width: 160 mm
Thickness: 21 mm
Weight
606 gr
ISBN-13
978-94-010-4896-5 (9789401048965)
DOI
10.1007/978-94-011-2026-5
Schweitzer Classification
Other editions
Additional editions
R.P. Agarwal | Patricia J.Y. Wong
Error Inequalities in Polynomial Interpolation and Their Applications
E-Book
12/2012
Springer
€53.49
Available for download
R.P. Agarwal | Patricia J.Y. Wong
Error Inequalities in Polynomial Interpolation and Their Applications
Book
06/1993
1st Edition
Kluwer Academic Publishers
€115.50
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Content
1 Lidstone Interpolation.- 1.1 Introduction.- 1.2 Lidstone Polynomials.- 1.3 Interpolating Polynomial Representations.- 1.4 Error Representations.- 1.5 Error Estimates.- 1.6 Lidstone Boundary Value Problems.- References.- 2 Hermite Interpolation.- 2.1 Introduction.- 2.2 Interpolating Polynomial Representations.- 2.3 Error Representations.- 2.4 Error Estimates.- 2.5 Some Applications.- References.- 3 Abel 7#x2014; Gontscharoff Interpolation.- 3.1 Introduction.- 3.2 Interpolating Polynomial Representations.- 3.3 Error Representations.- 3.4 Error Estimates.- 3.5 Some Applications.- References.- 4 Miscellaneous Interpolation.- 4.1 Introduction.- 4.2 (n, p) and (p, n) Interpolation.- 4.3 (0, 0; m, n - m) Interpolation.- 4.4 (0; m, n - m) Interpolation.- 4.5 (0, 2, 0; m, n - m) Interpolation.- 4.6 (0 : l - 1, l : l + j - 1; m, n - m) Interpolation.- 4.7 (0; Lidstone) Interpolation.- 4.8 (0, 2, 0; Lidstone) Interpolation.- 4.9 (1, 3, 0, 1; Lidstone) Interpolation.- 4.10 (0 : l - 1, l : l + j - 1; Lidstone) Interpolation.- 4.11 (0, 2, 1; Lidstone) Interpolation.- References.- 5 Piecewise - Polynomial Interpolation.- 5.1 Introduction.- 5.2 Preliminaries.- 5.3 Piecewise Hermite Interpolation.- 5.4 Piecewise Lidstone Interpolation.- 5.5 Two Variable Piecewise Hermite Interpolation.- 5.6 Two Variable Piecewise Lidstone Interpolation.- References.- 6 Spline Interpolation.- 6.1 Introduction.- 6.2 Preliminaries.- 6.3 Cubic Spline Interpolation.- 6.4 Quintic Spline Interpolation: ? = 4.- 6.5 Approximated Quintic Splines: ? = 4.- 6.6 Quintic Spline Interpolation: ? = 3.- 6.7 Approximated Quintic Splines: ? = 3.- 6.8 Cubic Lidstone - Spline Interpolation.- 6.9 Quintic Lidstone - Spline Interpolation.- 6.10 L2 - Error Bounds for Spline Interpolation.- 6.11 TwoVariable Spline Interpolation.- 6.12 Two Variable Lidstone - Spline Interpolation.- 6.13 Some Applications.- References.- Name Index.