Error Inequalities in Polynomial Interpolation and Their Applications

Inhaltsverzeichnis

• 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.
• 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.
• 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.
• 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.
• 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.
• Name Index.