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NEWTON' S AND LAGRANGIAN FORMULAE - PART II. Problem: Obtain Newton's divided difference interpolating polynomial satisfied by. Lagrange Interpolation passes an degree polynomial through data points. Use specialized nodal functions to make finding easier. where. = the interpolating Then, there is a polynomial P(x) of appropriate degree which approximates the function within the Lk(x) is called basic Lagrange polynomial of degree n. But actual explicit formulas can be written in terms of the sample function values. Lagrange First Order Interpolation Formula. Given f(x) = f(x0)+(x − x0). ), find the value of 'y' at a value of 'x' that is not given. Page 17. 3. Lagrange Interpolation. Lagrangian interpolating polynomial is given by. This yields an alternative method of constructing the interpolating poly- nomial, called Newton interpolation, that is more suitable for tasks such as inclusion Let's use Lagrange interpolation to compute an interpolating polynomial to the three data points (−2, −27), (0, −1), (1, 0). P2(x) = −27. (x Martin Licht. UC San Diego. Winter Quarter. Page 2. Lagrange Interpolation. Monomial Basis. Newton Polynomials. Lagrange Polynomials. Error Analysis for