Error Inequalities in Polynomial Interpolation and Their Applications: 262 (Mathematics and Its Applications, 262) - Softcover
Synopsis
This volume, which presents the cumulation of the authors' research in the field, deals with Lidstone, Hermite, Abel--Gontscharoff, Birkhoff, piecewise Hermite and Lidstone, spline and Lidstone--spline interpolating problems. Explicit representations of the interpolating polynomials and associated error functions are given, as well as explicit error inequalities in various norms. Numerical illustrations are provided of the importance and sharpness of the various results obtained. Also demonstrated are the significance of these results in the theory of ordinary differential equations such as maximum principles, boundary value problems, oscillation theory, disconjugacy and disfocality.
For mathematicians, numerical analysts, computer scientists and engineers.
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Error Inequalities in Polynomial Interpolation and Their Applications
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ISBN 10: 9401048967
ISBN 13: 9789401048965
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Taschenbuch. Condition: Neu. This item is printed on demand - it takes 3-4 days longer - Neuware -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. 380 pp. Englisch. Seller Inventory # 9789401048965
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Error Inequalities in Polynomial Interpolation and Their Applications
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Condition: New. Dieser Artikel ist ein Print on Demand Artikel und wird nach Ihrer Bestellung fuer Sie gedruckt. Preface. 1. Lidstone Interpolation. 2. Hermite Interpolation. 3. Abel--Gontscharoff Interpolation. 4. Miscellaneous Interpolation. 5. Piecewise--Polynomial Interpolation. 6. Spline Interpolation. Name Index.Given a function x(t) E c{n) [a, bj, points. Seller Inventory # 5831649
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Error Inequalities in Polynomial Interpolation and Their Applications
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Taschenbuch. Condition: Neu. This item is printed on demand - Print on Demand Titel. Neuware -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.Springer-Verlag KG, Sachsenplatz 4-6, 1201 Wien 380 pp. Englisch. Seller Inventory # 9789401048965
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Error Inequalities in Polynomial Interpolation and Their Applications
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Taschenbuch. Condition: 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. Seller Inventory # 105580520
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Taschenbuch. Condition: 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. Seller Inventory # 9789401048965
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Error Inequalities in Polynomial Interpolation and Their Applications (Mathematics and Its Applications, 262)
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