MATLAB Implementation of Interpolation and Fitting: Practical Code Solutions

For beginners' convenience, this resource provides MATLAB implementation methods for interpolation and fitting, ideal for students working on course projects. Interpolation and fitting constitute crucial components of numerical analysis with broad practical applications. Interpolation involves constructing a continuous function within an interval based on known discrete data points, facilitating computational operations. Curve fitting refers to identifying optimal parameters within a function's parameter space to best approximate the given discrete data points.

MATLAB provides powerful built-in functions for these operations: For interpolation, commonly used functions include interp1 for one-dimensional interpolation (with methods like 'linear', 'spline', 'pchip'), and interp2 for two-dimensional data. Polynomial interpolation can be implemented using polyfit and polyval functions. For curve fitting, the Curve Fitting Toolbox offers fit function supporting various model types (polynomial, exponential, Fourier series), while basic fitting can be performed using polyfit for polynomial regression or lsqcurvefit for nonlinear least-squares fitting.

Key implementation considerations include: selecting appropriate interpolation methods based on data characteristics (linear for speed, spline for smoothness), determining optimal polynomial degrees for fitting to avoid overfitting, and evaluating fit quality using metrics like R-squared and RMSE. These methods enable more effective analysis and solution of practical problems, significantly enhancing work efficiency in data processing and mathematical modeling tasks.