assign7 - n dimensions as discussed in class Test your code...

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ASE 211 Homework 7 Due: In class, Monday, March 21st. 1. Take 4 iterations of Newton’s method by hand for solving the nonlinear equations discussed in class, starting with initial guess x 0 = (1 , 0) . Speciﬁcally, F ( x 1 , x 2 ) = " x 3 1 + x 2 - 1 x 1 + x 2 # J = " 3 x 2 1 1 1 1 # With initial guess (1 , 0) , solve Js = " 3 1 1 1 # " s 1 s 2 # = - F = " 0 - 1 # to get s = ( 1 2 , - 3 2 ) , and x 1 = x 0 + s = " 3 2 - 3 2 # Continue for 3 more iterations. Repeat now with the initial guess x 0 = (0 , - 1) : Js = " 0 1 1 1 # " s 1 s 2 # = - F = " 2 1 # to get s = ( - 1 , 2) , and x 1 = x 0 + s = " - 1 1 # Continue for 3 more iterations. 2. Write a matlab code newtonrn.m which implements Newton’s method in
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Unformatted text preview: n dimensions ( as discussed in class ). Test your code on the function in problem 1. Take your tolerances F tol and s tol as 10-5 and set the maximum number of iterations to 100. Use the initial condition x = (1 ,-1) . How many Iterations were required for convergence? What was the value of k F k and k s k when convergence was attained?...
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