Piecewise Least Squares Algorithm for Curve Fitting

This text describes a highly useful algorithm—the piecewise least squares algorithm—applicable to curve fitting. By implementing this algorithm, we can partition a model into multiple segments for fitting, thereby improving both accuracy and precision. The core implementation typically involves dividing data points into optimal intervals using change-point detection (e.g., via residual analysis or genetic algorithms), then applying standard least squares regression to each segment. Key functions may include dynamic programming for optimal breakpoint selection and matrix operations for efficient coefficient calculation. In practical terms, the algorithm processes data points segmentally during fitting to better capture trends and local variations. Furthermore, it finds applications in signal processing (e.g., piecewise signal approximation), image processing (e.g., edge-aware filtering), and machine learning (e.g., regime-switching models). Thus, mastering this algorithm is essential for scientists and engineers working with complex, non-uniform datasets.