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Unformatted text preview: Math 174/274 Final March 16, 2009 • Please put your name, ID number, and sign and date. • There are 8 problems worth a total of 200 points. • You must show your work to receive credit . Print Name: Student ID: Signature and Date: Problem Score 1 /25 2 /25 3 /25 4 /25 5 /25 Problem Score 6 /25 7 /25 8 /25 Total /200 1 1. (25 pts) Suppose f is continuous and we know that f ( x ) > 0 in [ 1 , 2] and f ( x ) < in [2 . 5 , 4]. (a) Find three approximations to the root of f ( x ) using the bisection method with starting interval [ 1 , 4]. (b) Find the best bound you can for the absolute error of the third approximation. 2 2. (25 pts) Use the Gaussian elimination process with row pivoting and back substitu tion to solve A~x = ~ b when A = 2 1 2 2 1 4 3 . and ~ b = [2 , 4 , 2]. 3 3. (25 pts) Consider A~x = ~ b with A = 3 1 1 1 2 and ~ b = [1 , 2 , 2] t . (a) Determine if Jacobi method will converge to the solution of this system for any initial guess. (b) Perform one iteration of Jacobi method with initial guess ~x (0) = [1 , 1 , 1] t ....
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This note was uploaded on 10/17/2010 for the course MATH 174 taught by Professor Staff during the Spring '08 term at UCSD.
 Spring '08
 staff
 Math

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