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Unformatted text preview: Homework 4 Foundations of Computational Math 2 Spring 2011 Solutions will be posted Monday, 2/7/11 Problem 4.1 Suppose we want to approximate a function f ( x ) on the interval [ a, b ] with a piecewise quadratic interpolating polynomial with a constant spacing, h , of the interpolation points a = x < x 1 . . . < x n = b . That is, for any a x b , the value of f ( x ) is approximated by evaluating the quadratic polynomial that interpolates f at x i 1 , x i , and x i +1 for some i with x = x i + sh , x i 1 = x i- h , x i +1 = x i + h and- 1 s 1. (How i is chosen given a particular value of x is not important for this problem. All that is needed is the condition x i 1 x x i +1 .) Suppose we want to guarantee that the relative error of the approximation is less than 10 d , i.e., d digits of accuracy. Specifically, | f ( x )- p ( x ) | | f ( x ) | 10 d ....
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This note was uploaded on 11/10/2011 for the course MAD 5404 taught by Professor Gallivan during the Spring '11 term at FSU.
- Spring '11