Since the product skips m = j, when i = j then all terms are / =1Īlso, when i ≠ j, m ≠ j does not produce it and one term in the product will be for m = I, that is, / = 0 Now, consider what happens when this product is expanded. L j(x) contains k factors in product and each factor has x.Let’s assume a function L(x j) such that L(x j) = y j, j = 0, 1, 3, 3. (x k, y k) where each points are distinct. Derivation of Lagrange Interpolation:Ĭonsider a given set of k+1 points, (x 0, y 0), (x 1, y 1), ( x 2, y 2)…. You can also check out our earlier tutorial where we discussed a C program for this interpolation technique. In this tutorial, we’re going to write a program for Lagrange Interpolation in MATLAB, and go through its mathematical derivation along with a numerical example. Lagrange Polynomial Interpolation is useful in Newton-Cotes Method of numerical integration and in Shamir’s secret sharing scheme in Cryptography. In a set of distinct point and numbers x j and y j respectively, this method is the polynomial of the least degree at each x j by assuming corresponding value at y j. Named after Joseph Louis Lagrange, Lagrange Interpolation is a popular technique of numerical analysis for interpolation of polynomials.
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