One-Dimensional Moving Least Squares (MLS) Matlab Implementation

This document presents a comprehensive MATLAB implementation of the one-dimensional Moving Least Squares (MLS) method for sophisticated curve fitting applications. The program employs weighted least squares approximation with moving local domains, where the weight function typically uses Gaussian or spline-based kernels to emphasize nearby data points. Users can leverage this implementation to achieve superior fitting accuracy through adaptive local approximations that effectively handle non-uniform data distributions. Prior to utilization, familiarity with fundamental curve fitting concepts is recommended, as MLS operates by constructing local polynomial approximations at each evaluation point while smoothly blending these local fits through continuous weight functions. The algorithm excels in noise reduction and irregularity smoothing through its inherent localization properties, automatically adapting to local data characteristics. Key programmable parameters include the influence domain radius, polynomial basis order (linear/quadratic), and weight function parameters - all configurable to optimize fitting performance for specific datasets. The implementation features modular function design with separate routines for weight calculation, local matrix assembly, and weighted least squares solution, enabling easy customization for specialized applications.