Chapter 5
Interpolation
This chapter develops methods for estimating values between known data points. It introduces polynomial interpolation in Lagrange and Newton divided-difference forms, including forward and backward formulas for equally spaced data. It then examines interpolation error, the Runge phenomenon, and the use of Chebyshev nodes, before introducing cubic splines as a piecewise-polynomial alternative. The chapter closes by distinguishing interpolation from data fitting and presenting practical guidelines for choosing a method.
In this chapter
- 5.1 What interpolation does
- 5.2 General polynomial interpolation
- 5.3 Spline interpolation
- 5.4 Interpolation versus data fitting
- 5.5 Summary and practical guidelines
- 5.6 Computational exercises and projects
Companion resources
Codes
MATLAB, Python, C++, and Fortran programs that implement polynomial interpolation, including interpolation at Chebyshev nodes, and cubic-spline interpolation.
View Chapter 5 codes →Exercises & Projects
Additional exercises for practice and homework, together with physics projects that apply interpolation to tabulated physical data and larger computational problems.
View Chapter 5 exercises & projects →Resources
Interpolation-library links, method-selection guidance, practical notes, and selected references for further study.
View Chapter 5 resources →Updates & Errata
Corrections, clarifications, and post-publication updates associated with Chapter 5.
View Chapter 5 updates & errata →