Lagrange Function: A MATLAB Implementation

In mathematics and engineering fields, Lagrange interpolation serves as a fundamental concept. This method constructs a polynomial function that passes exactly through given data points (x,y coordinates) to approximate the underlying curve. MATLAB provides built-in capabilities for Lagrange interpolation through functions like polyfit and polyval, enabling efficient polynomial curve fitting. The implementation typically involves calculating Lagrange basis polynomials using the formula: L(x) = Σ [y_i * Π (x - x_j)/(x_i - x_j)] where the product excludes j=i terms. This can be programmed as a reusable MATLAB function that accepts coordinate vectors and returns interpolation coefficients or evaluated points. Key advantages of using a pre-built Lagrange function include: - Simplified polynomial computation without manual calculations - Efficient handling of varying dataset sizes through vectorized operations - Time-saving implementation using MATLAB's optimized numerical routines - Direct application through function calls like lagrange_interp(x_data, y_data, x_query) The function can incorporate error checking for duplicate x-values and provide options for different output formats (coefficients or interpolated values), making it suitable for both educational and professional applications in signal processing, data analysis, and numerical modeling.