# National Interpolating Polynomial

by Gilmar

National Interpolating Polynomial

Given the following three data points:

x    -1     0     1
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F(x)    1    -1    -1

Determine the national interpolating polynomial of lowest degree possible to this data using

a. Lagrange’s interpolation formula,

b. Newton’s interpolation formula

c. Quote the formula for the error applied to these special cases (since you are not given f(x), just leave any term’s in the error formula involving f(x) as they are)

### Comments for National Interpolating Polynomial

 Mar 21, 2013 Polynomial by: Staff Answer Part I I didn't work out the entire problem, but I did determine the function f(x) for you using the Vandermonde Approach. The 2nd degree polynomial function passing through the three points is: Vandermonde Approach The standard form of an Interpolating Polynomial for three data points is the following second degree polynomial. Once the values of the coefficients have been determined, the function can be used to evaluate other values of x (in addition to the three data points given). Determine the value of the coefficients a₁,a₂, and a₃ as follows: Evaluate the function for the data point (-1, 1) --------------------------------------------------

 Mar 21, 2013 Polynomial by: Staff -------------------------------------------------- Part II Evaluate the function for the data point (0, -1) Evaluate the function for the data point (1, -1) Solve the three equations for the coefficients a₁,a₂, and a₃ since the value of a₁ = -1, substitute -1 for the coefficient a₁ in all equations --------------------------------------------------

 Mar 21, 2013 Polynomial by: Staff -------------------------------------------------- Part III Solve for a₃ using addition / elimination substitute -1 for a₁, and 1 for a₃ solve for a₂ substitute the numerical values of all three coefficients for the letter values (a₁, a₂, and a₃) in the standard form of the original Interpolating Polynomial Thanks for writing. Staff www.solving-math-problems.com