Assignment 3

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
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