ASE 211 - Homework 7 Due Mar. 19

ASE 211 - Homework 7 Due Mar. 19 - newtonrn.m which...

This preview shows page 1. Sign up to view the full content.

ASE 211 Homework 7 Due: In class, Wednesday, March 19th. 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 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
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: newtonrn.m which implements Newton’s method in 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 || F || and || s || when convergence was attained?...
View Full Document

This note was uploaded on 09/18/2011 for the course ASE 211 taught by Professor N/a during the Spring '08 term at University of Texas at Austin.

Ask a homework question - tutors are online