advertisement

Math 230 Assignment 3 Submission of THIS assignment is NOT required. However, you are strongly encouraged to do this assignment yourself and check with Answer to be provided!! Interpolation and Polynomial, Exercise 3.1, p. 115 1. For the given function f ( x) 3 x 1 , let x0=1, x1=1.25 and x2=1.6. Construct interpolation polynomials of degree at most one (P1) and at most two (P2) to approximate f(1.4), and find the absolute error. Use theorem 3.3 to find an error bound for the approximation. 2. Suppose xj=j, for j=0,1,2,3 and it is known that P0,1(x)=x+1, P1,2(x)=3x-1 and P1,2,3(1.5)=4. Find P0,1,2,3 (1.5). . Divided Difference 3.2, p. 127 1. Use Newton’s divided –difference to construct interpolation polynomials of degree one, two, and three for the following data. Approximate the specified value using each of the polynomials. f(0)if f(-0.5)=1.93750, f(-0.25)=1.33203, f(0.25)=0.800781, f(0.5)=0.687500