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Unformatted text preview: Assigned: Monday Oct. 31, 2011 Due Date: Friday, Nov. 11, 2011 MATH 174/274: Homework VI “Polynomial Interpolation” Fall 2011 1. Consider the function f ( x ) = sin π 2 x + x 2 . (a) We would like to construct a polynomial P ( x ) that interpolates f ( x ) at the points x = 0, x 1 = 2, and x 2 = 3. Compute all the necessary Lagrange polynomials and use these to construct the interpolating polynomial P ( x ). (b) Compute the error term R ( x ). (c) Interpolation: Compute the maximum bound on R ( x ) if we approximate f (1) by P (1). (d) Extrapolation: Compute the maximum bound on R ( x ) if we approximate f (4) by P (4). 2. SOURCE CODE: Let x ,x 1 ,...,x n be distinct points with corresponding data values f ,f 1 ,...,f n . Let P ( x ) be the unique polynomial of degree n which interpolates the data (i.e., P ( x i ) = f i for each i = 0 ,...,n ). Write the following MATLAB routines: (a) F = DivDiff(x,f,n)- a function to compute the divided differences....
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This note was uploaded on 12/11/2011 for the course MATH 174 taught by Professor Staff during the Fall '08 term at UCSD.
- Fall '08