midtermtwo174W09

# midtermtwo174W09 - guess ~x =[1 1 1 1 1 t 3 3(25 pts...

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Math 174/274 Midterm 2 February 25, 2009 Please put your name, ID number, and sign and date. There are 4 problems worth a total of 100 points. Calculators are allowed but 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 Total /100 1

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1. (25 pts) (a) Use Gaussian elimination with row pivoting to ﬁnd the PLU factorization for the matrix A = 1 - 4 3 0 2 1 2 0 2 . (b) Explain how you can directly use the PLU factorization to solve the linear system A~x = ~ b in a fast way. 2
2. (25 pts) Consider the linear system A~x = ~ b with A = 2 0 0 0 - 1 0 - 2 0 - 1 0 - 2 0 4 0 1 0 0 0 - 1 0 0 2 0 0 3 . and b = [1 , 0 , - 1 , 0 , 2] t . Perform one iteration of Gauss-Seidel method using initial

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Unformatted text preview: guess ~x = [1 , 1 , 1 , 1 , 1] t . 3 3. (25 pts) Consider A~x = ~ b where A = ± a b c d ² . (a) Find conditions on bc/ad such that Jacobi method will converge for any initial guess. (b) Find conditions on bc/ad such that Gauss-Seidel method will converge for any initial guess. 4 4. (25 pts) Let p ( x ) be the polynomial of least degree interpolating the data points x-1 1-2 y 6 1 2 17 (a) Write out the Lagrange form for p ( x ). (b) Write out the Newton form for p ( x ). 5...
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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.

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midtermtwo174W09 - guess ~x =[1 1 1 1 1 t 3 3(25 pts...

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