Lagrange Interpolation MATLAB Source Code Implementation

In mathematics, Lagrange interpolation is a method used for interpolating between given data points. This approach is based on the fundamental principle that an nth-degree polynomial can be uniquely determined by n+1 distinct points. The core concept of Lagrange interpolation involves constructing an nth-degree polynomial that passes exactly through a given set of data points. To derive this polynomial, one typically solves a system of linear equations. MATLAB, as a widely-used programming language, provides an excellent platform for implementing Lagrange interpolation. Below is the MATLAB source code that demonstrates how to implement Lagrange interpolation and perform related mathematical computations. The implementation begins by defining sample data points: x = [1 2 3 4 5]; y = [3 4 9 12 20]; The lagrange function (which needs to be implemented separately) constructs the interpolation polynomial using Lagrange basis polynomials. Each basis polynomial is designed to be 1 at one data point and 0 at all others. To visualize the interpolation results: xx = linspace(1,5,100); creates 100 equally spaced points between 1 and 5 yy = polyval(p,xx); evaluates the polynomial at these points plot(x,y,'o',xx,yy) displays both original data points (circles) and the interpolation curve For practical interpolation calculation: x0 = 2.5; y0 = polyval(p,x0); computes the polynomial value at x=2.5 fprintf('在x=%f处的插值多项式的值为%fn',x0,y0) prints the result This MATLAB implementation demonstrates how to efficiently perform Lagrange interpolation, visualize the results, and compute specific values. The code utilizes MATLAB's built-in functions like polyval for polynomial evaluation and linspace for generating interpolation ranges. The algorithm can be easily extended to handle larger datasets and different interpolation requirements. Other programming languages and mathematical software packages can also implement this method using similar algorithmic approaches.