May 2020
Intermediate to advanced
656 pages
16h 6m
English
book
Applied Numerical Methods Using MATLAB, 2nd Edition
by Won Y. Yang, Wenwu Cao, Jaekwon Kim, Kyung W. Park, Ho-Hyun Park, Jingon Joung, Jong-Suk Ro, Han L. Lee, Cheol-Ho Hong, Taeho Im
Content preview from Applied Numerical Methods Using MATLAB, 2nd Edition
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3Interpolation and Curve Fitting
Chapter Outline
- 3.1 Interpolation by Lagrange Polynomial
- 3.2 Interpolation by Newton Polynomial
- 3.3 Approximation by Chebyshev Polynomial
- 3.4 Pade Approximation by Rational Function
- 3.5 Interpolation by Cubic Spline
- 3.6 Hermite Interpolating Polynomial
- 3.7 Two‐Dimensional Interpolation
- 3.8 Curve Fitting
- 3.9 Fourier Transform
There are two topics to be dealt with in this chapter, interpolation1 and curve fitting. Interpolation is to connect discrete data points in a plausible way so that one can get reasonable estimates of data points between the given points. The interpolation curve goes through all data points. Curve fitting, on the other hand, is to find a curve that could best indicate the trend of a given set of data. The curve does not have to go through the data points. In some cases, the data may have different accuracy/reliability/uncertainty and we need the weighted least squares (WLS) curve fitting to process such a data.
3.1 Interpolation by Lagrange Polynomial
For a given set of N + 1 data points {(x0, y0), (x1, y1), …, (xN, yN)}, we want to find the coefficients of an Nth‐degree polynomial function to match them:
The coefficients can be obtained ...
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