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# Mon_short - Math 151A Final Exam:30 am-2:30 pm [email protected]

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Math 151A Final Exam March 19, 11:30 am -2:30 pm, 2001 @UCLA PRINT NAME: I acknowledge and accept the honor code. SIGN NAME: No books No notes No calculators 10 problems 100 points Please do any 8 problems 180 minutes Show work Good Luck! SCORE: 1 2 3 4 5 6 7 8 9 10 Total 1

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1. (10 points) Short answer questions: a Give the relation between errors e n +1 and e n , where e n := | p n - p | , asso- ciated with Newton’s method for solving non-linear equations. (You can use a constant C to represent any derivative which occur in this relation.) b As an approximation method, is numerical differentiation stable? why or why not? c A linear system Ax = 0 has a unique solution x = 0, does the system Ax = b has unique solution for any given b ? d Assume a given function f C [ a, b ]. How many points would you use to construct a Lagrange polynomial of degree 10? 2. (10 points) Newton’s method is used to find a solution to p = p - f ( p ) /f ( p ) based on an initial approximation p 0 . Given the tolerance TOL and the maxi-
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Mon_short - Math 151A Final Exam:30 am-2:30 pm [email protected]

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