INTERPOLAÇÃO POLINOMIAL - MÉTODO DE LAGRANGE | 07

Polynomial Interpolation - Lagrange Method Polynomial Interpolation by the Lagrange Method Interpolation – Lagrange Methods The Lagrange technique provides an alternative way to calculate the same polynomial that passes through the three points using three distinct functions (which are also polynomials), a function L i ( x ) L_i(x) Li(x) corresponding to each point ( x i , y i ) x_i,y_i) xi,yi), which have well-defined characteristics. What is Lagrange interpolation? It consists of determining a function g(x) that approximately describes the behavior of another function f(x) that is unknown. Some tabulated values ​​of the type (x, f(x)) are known. What is a Lagrange interpolating polynomial? Image result for Polynomial Interpolation by Lagrange's Method In numerical analysis, the Lagrange polynomial (named after Joseph-Louis de Lagrange) is the interpolation polynomial of a set of points in Lagrange form. How does polynomial interpolation work? Polynomial interpolation aims to approximate functions (tabulated or given by equations) by polynomials of degree up to n. This is intended to facilitate the calculation of functions at points that are not given (interpolation means calculating internal points that are not given). How to calculate the interpolating polynomial? Since the set consists of 4 points, the interpolating polynomial must be of the form: p ( x ) = a 0 + a 1 x + a 2 x 2 + a 3 x 3 . whose solution is a 0 = 1 , a 1 = 6 , a 2 = 0 and a 3 = − 1 . Therefore, the interpolating polynomial is p ( x ) = 1 + 6 x − x 3 . polynomial interpolation, linear interpolation, quadratic interpolation, lagrange interpolation, polynomial interpolation applications, interpolating polynomial of degree 2, lagrange method exercises, interpolating polynomial, Polynomial Interpolation, Lagrange Method, Polynomial Interpolation, Lagrange, Lagrange Polynomial, Interpolating Polynomial, Lagrange Interpolating Polynomial, Lagrange Interpolating Polynomial, Lagrange Interpolating Polynomial, Numerical Calculus