Strain Computation

Local Least Squares Fitting is a computational method used for data approximation. This technique operates by fitting a quadratic function within each local region of the dataset to approximate the entire data distribution. The algorithm effectively handles noise and irregularities in data while providing smooth curve fitting. Key implementation aspects include:

Algorithm Steps: 1. Define a sliding window size to determine local neighborhoods 2. For each data point, solve the normal equations: (X^T X)β = X^T y 3. Compute quadratic coefficients using matrix operations: β = (X^T X)^(-1) X^T y 4. Apply regularization to handle ill-conditioned matrices 5. Implement boundary handling for edge points

Common applications include data analysis, curve fitting, and pattern recognition. The method is particularly valuable in engineering applications where smooth strain curves need to be derived from discrete measurement points. MATLAB implementation typically utilizes built-in functions like polyfit() within moving window loops, or custom functions leveraging backslash operators for efficient least squares solutions.