POLYNOMIAL INTERPOLATION - LAGRANGE METHOD
Polynomial Interpolation - Lagrange's Method
Polynomial Interpolation by the Lagrange's Method
Interpolation - Lagrange's 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 interpolation 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 (tabled or given by equations) by polynomials of degree up to n. This is intended to facilitate the calculation of functions at non-given points (interpolation means calculating internal non-given points).
How do you calculate the interpolating polynomial?
Since the set consists of four 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 .
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