Error Inequalities in Polynomial Interpolation and Their Applications

By: Patricia J. Y. Wong, Ravi P. Agarwal

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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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Preface
Lidstone Interpolation
Lidstone Polynomials	p. 2
Interpolating Polynomial Representations	p. 17
Error Representations	p. 17
Error Estimates	p. 19
Lidstone Boundary Value Problems	p. 21
Hermite Interpolation
Interpolating Polynomial Representations	p. 63
Error Representations	p. 71
Error Estimates	p. 91
Some Applications	p. 149
Abel - Gontscharoff Interpolation
Interpolating Polynomial Representations	p. 173
Error Representations	p. 175
Error Estimates	p. 178
Miscellaneous Interpolation
(n,p) and (p,n) Interpolation	p. 192
(0, 0; m,n - m) Interpolation	p. 198
(0; m,n - m) Interpolation	p. 203
(0, 2, 0; m, n - m) Interpolation	p. 206
(0 : l - 1, l : l + j - 1; m, n - m) Interpolation	p. 208
(0; Lidstone) Interpolation	p. 209
(0, 2, 0; Lidstone) Interpolation	p. 210
(1, 3, 0, 1; Lidstone) Interpolation	p. 211
(0 : l - 1, l : l + j - 1; Lidstone) Interpolation	p. 213
(0, 2, 1; Lidstone) Interpolation	p. 214
Piecewise - Polynomial Interpolation
Piecewise Hermite Interpolation	p. 228
Piecewise Lidstone Interpolation	p. 257
Two Variable Piecewise Hermite Interpolation	p. 266
Two Variable Piecewise Lidstone Interpolation	p. 274
Spline Interpolation
Cubic Spline Interpolation	p. 285
Quintic Spline Interpolation : [tau] = 4	p. 290
Approximated Quintic Splines : [tau] = 4	p. 301
Quintic Spline Interpolation : [tau] = 3	p. 309
Approximated Quintic Splines : [tau] = 3	p. 315
Cubic Lidstone - Spline Interpolation	p. 321
Quintic Lidstone - Spline Interpolation	p. 323
L[subscript 2] - Error Bounds for Spline Interpolation	p. 327
Two Variable Spline Interpolation	p. 334
Two Variable Lidstone - Spline Interpolation	p. 346
Name Index	p. 363
Table of Contents provided by Blackwell. All Rights Reserved.

Error Inequalities in Polynomial Interpolation and Their Applications

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Hardcover

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