March 2014
Intermediate to advanced
412 pages
11h 16m
English
Content preview from Numerical Methods and Optimization
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112 Numerical Methods and Optimization: An Introduction
4.19. Consider the system of equations
x
2
+ y
2
− 9=0
x + y − 1=0.
Apply Newton’s method twice with starting point [1, 0]
T
. Show the exact
solutions and the steps of Newton’s method graphically.
4.20. Use Newton’s method twice with initial guess [x
0
,y
0
]
T
=[1/2, 0]
T
to
solve the nonlinear system
x
2
− x − y =0
x + y − 2=0.
Illustrate your steps graphically.
4.21. Consider the system of equations
x
4
+ y
4
− 3=0
x
3
− 3xy
2
+1 = 0.
Apply Newton’s method twice with the starting point [1, 1]
T
.
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