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Unformatted text preview: Homework 9 Foundations of Computational Math 2 Spring 2011 Solutions will be posted Friday, 3/25/11 Problem 9.1 In this problem we consider the numerical approximation of the integral I = integraldisplay 1 1 f ( x ) dx with f ( x ) = e x . In particular, we use a priori error estimation to choose a step size h for Newton Cotes or a number of points for a Gaussian integration method. 9.1.a Consider the use of the composite Trapezoidal rule to approximate the integral I . Use the fact that we have an analytical form of f ( x ) to estimate the error using the composite trapezoidal rule and to determine a stepsize h so that the error will be less than or equal to the tolerance 10 2 . Approximately how many points does your h require? 9.1.b Consider the use of the Gauss-Legendre method to approximate the integral I . Use n = 1, i.e., two points x and x 1 with weights and 1 ....
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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