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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
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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 105 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?...
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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.
 Spring '08
 N/A

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