Least Squares Surface Fitting Program (MATLAB Implementation)

This document presents a MATLAB-based least squares surface fitting program (m-file) designed to fit three-dimensional data z = f(x, y). The program approximates the relationship between z and x,y using polynomial functions, generating a smooth surface ideal for data visualization and analysis. The implementation utilizes matrix operations to solve the normal equations derived from minimizing the sum of squared residuals between the data points and the fitted surface. Key algorithmic features include: constructing the design matrix based on polynomial terms of x and y, solving the linear system using MATLAB's backslash operator or pinv() function for numerical stability, and generating coefficient estimates for the polynomial expansion. Users can input their 3D dataset and the program will compute and output the fitting results, facilitating better understanding of data characteristics and trends. The program supports customizable parameters including polynomial degree selection, regularization options, and fitting constraints to accommodate various application scenarios. The implementation handles different polynomial orders (linear, quadratic, cubic, etc.) through systematic term generation and coefficient calculation. Using this least squares surface fitting program significantly enhances data analysis efficiency and accuracy while providing reliable surface approximations for engineering and scientific applications.