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Unformatted text preview: Assigned: Friday Oct. 7, 2011 Due Date: Friday Oct. 14, 2011 MATH 174: Homework III ”Linear Algebra (Part I)” Fall 2011 1. The function f ( x ) = cos( x ) has a root at x = π/ 2. Using the theory we developed for fixed point iterations , find the largest interval around x = π/ 2 in which we can choose an initial guess for Newton’s method and still be guaranteed to converge to π/ 2. 2. Show that the iteration scheme α n +1 = g ( α n ) = α 2 n aα n + a 2 + 5 a α n + 5 , n ≥ converges to the fixed point a quadratically (i.e., order of convergence is 2) for all a 6 = 5. ( HINT: subtract a from both sides, manipulate the expression so that it has the same form as in the definition of order of convergence, then take the limit as n → ∞ . Note that α n → a as n → ∞ . This problem is very similar to Problem #4 of Project #1.) 3. Consider the following 2 matrices, A = a b c d , B = 1 2 2 1 ....
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This note was uploaded on 12/11/2011 for the course MATH 174 taught by Professor Staff during the Fall '08 term at UCSD.
 Fall '08
 staff
 Linear Algebra, Algebra

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