In numerical analysis, the Lagrange interpolating polynomial is the unique polynomial of lowest degree that interpolates a given set of data. Lagrange interpolation formula, 192 Lagrange interpolation polynomial. The interpolation polynomial passes through all four control points, and each scaled basis polynomial passes through its respective control point and is 0 where x corresponds to the other three control points. symbolic routines for, 95 upper, 241 inhomogeneous Airy differential equation, 246. 2) Lagrange form is not convenient when: o additional data points may be added to the problem, or o appropriate degree of the interpolating polynomial is unknown i.e.
This image shows, for four points ( (−9, 5), (−4, 2), (−1, −2), (7, 9)), the (cubic) interpolation polynomial L( x) (dashed, black), which is the sum of the scaled basis polynomials y 0 ℓ 0( x), y 1 ℓ 1( x), y 2 ℓ 2( x) and y 3 ℓ 3( x). 1) The Lagrange Interpolation is particularly convenient when the same values of the independent variable x may occur in different applications (with only y values changed). Not to be confused with Legendre polynomials (the orthogonal basis of function space).
