Introduction to Numerical Analysis and Scientific Computing

Chapter 4

Polynomial Interpolation and Splines Fitting

4.1Definition of Interpolation

4.2General Lagrange Polynomial Interpolation

4.3Recurrence Formulae

4.3.1Neville’s Formula

4.3.2Newton’s Form for the Interpolation Polynomial

4.3.3Divided Differences Table and Newton’s Formula

4.4Equally Spaced Data: Difference Operators

4.5Errors in Polynomial Interpolation

4.6Local Interpolation: Spline Functions

4.6.1Linear Spline Interpolation

4.6.2Quadratic Spline Interpolation

4.6.3Cubic Spline Interpolation

4.6.4Solving a Tridiagonal System

4.6.5Errors in Spline Interpolation

4.7Concluding Remarks

4.8Exercises

4.9Computer Projects

4.1 Definition of Interpolation

Consider a set D_n of n + 1 data points in the (x, y) plane:

$D_n=(x_i$