Question

What are pros and cons of each of the following Polynomial Interpolation Methods:

1. Vandermonde

2. Lagrange

3. Newton

Answer 1

Pros of Vandermonde interpolation method Polynonual is very Cost to evaluate the coefficients are known. cheap 20 Availability of derivatives is very easy cons of Vandermonde interpolation method in Cost to determine the polynomial is very costly, since a dense linear system has to be solved Q: incremental interpolaron is not supported, Scanned with CamScanner

Pros of Lagrange's interpolation method • The answers for higher order more accurate polynomials will be • used in Simultaneous optimization of nowns of derivative of lagrange polynomials, • The error decreases by ant if we decrease the distance between interpolatton pounts by 2, where n is the order of lagrange polynomial. • There is no need to consbuck the divided difference Hebde. • For higher order polynomials the approximate result converges to the exact solution quickly. Cons of Lagrange's Interpolation method lo Higher polynomials require more time to compute 2. 16 becomes difficult when the polynomial order increases because the namber of Points increases and we need to evaluate appro rumake Soutons for each Point 3. To increase degree of the addition of another inter Scoton leads to re-computation. s

Pros of Newtons nierpolation method To This method is very fast and Slimmple to apply 2. Newton's method is good al fending a local minimum 3. Newton's method produces excellent local convergence. Cons of Newton's interpolation methoel to Newton's method is not a global method. 2. } Convergence is not guaranteed even if the uncertaisita interval is known. 3. This method is Scanned with CamScanner computationally CS sca expensive