MATLAB Implementation of Interpolation Algorithms and Curve Fitting with Code Examples

Implementing interpolation algorithms and curve fitting in MATLAB provides powerful capabilities for numerical analysis and data processing. These two techniques have distinct characteristics and are suitable for different application scenarios. Interpolation algorithms are primarily used to estimate values between known discrete data points. MATLAB offers multiple interpolation methods: - Linear interpolation is the simplest form, connecting adjacent data points with straight lines using the interp1 function with 'linear' method - Cubic spline interpolation produces smoother curves using the spline function or interp1 with 'spline' option - Polynomial interpolation constructs polynomial functions passing through all given points using polyfit and polyval functions for evaluation Curve fitting involves finding a mathematical model that best matches the data without necessarily passing through all points, but capturing the overall trend: - Polynomial fitting is the most commonly used method, implemented via polyfit function which returns polynomial coefficients - Nonlinear fitting handles more complex data patterns using fit function from Curve Fitting Toolbox or lsqcurvefit for optimization - Least squares method serves as the most prevalent optimization criterion, minimizing the sum of squared residuals between data and model In practical applications, interpolation is suitable when exact reproduction of known data points is required, while fitting is better for handling noisy data or predicting trends. MATLAB's extensive toolbox provides rich functions like interp1, spline, polyfit, fit, and lsqcurvefit, allowing users to select appropriate methods based on data characteristics and application requirements. Key implementation considerations include choosing proper polynomial degrees, handling boundary conditions in splines, and selecting convergence criteria for nonlinear fits.