Ee1037b2S10

Ee1037b2S10 - f ( x) 0 Newton's Algorithm Newton's Method:...

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Newton’s Method: Square Systems () 0 fx Newton’s Algorithm Select an initial vector x Whil ( i t t i diti h t d) DoWhile (some appropriate stopping condition has not occurred) Compute the Jacobian, () f Jx Let y solve the system of linear equations f yf x  (assuming f is nonsingular) x x y  End DoWhile variable , '( ) 0 function of one f x Fact: Assume k x x , and f is nonsingular (the n -dimensional analog of '( ) 0 ). Then the rate of convergence is quadratic. EE 103 Slides 7B2 (SEJ) 1
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Gauss Newton Method: Non Square Systems (m > n) Gauss-Newton Algorithm (Does not always work) () 0 f x Select an initial vector x DoWhile (some appropriate stopping condition has not occurred) ompute ) x d e cobian ) x Compute () fx and the Jacobian, f Jx Let y solve the system of linear equations ( () () ) ()() TT ff f y f x  (assuming (( ) ) f rank J x n ) xx y  End DoWhile EE 103 Slides 7B2 (SEJ) 2
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Optimization (Steepest Descent) min ( ) n xR gx Steepest Descent Algorithm (general idea) Select an initial vector n DoWhile
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This note was uploaded on 06/01/2010 for the course EE EE 103 taught by Professor Jacobsen during the Spring '09 term at UCLA.

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Ee1037b2S10 - f ( x) 0 Newton's Algorithm Newton's Method:...

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