Fall 2011  PGE 310: Formulation and Solution in Geosystems Engineering
HW #9: System of Linear Equations by Iterative Methods  System of NonLinear Equations by Newton’s Method
Due Date:
Thursday Nov 10
th
2011
Do NOT forget to follow the guideline for submitting homework
(Attached to the end of this file)
1.
System of Linear Equations – Iterative Methods
(By HAND)
Assume that in your Static Exam, you are asked to figure out the support forces of the structure below.
(
?
?,
?,
3
2
1
F
F
F
)
After writing the force and the moment equilibrium equations, you ended up with the following system of linear
equations:
10
6
2
6
4
2
13
3
5
3
2
1
3
2
1
3
2
1
F
F
F
F
F
F
F
F
F
a)
Determine if the coefficient matrix of this system is diagonally dominant, so that the convergence of iterative
methods is guaranteed.
b)
Determine
l
1
matrix norm
,
l
2
matrix norm
and
l
∞
matrix norm
of the coefficient matrix.
c)
Determine the
condition number
of the coefficient matrix. How many digits of precision will be lost in solving
this system of equations?
d)
Solve the system of equations for
3
2
1
,
F
and
F
F
using the initial guess
0
0
0
3
2
1
)
0
(
F
F
F
F
using the following
methods:
1.
Richardson Iteration using Q=I
2.
Jacobi Method
3.
GaussSeidel Method
4.
SOR (Successive Over Relaxation) Method with
2
.
1

Determine only the first two iterations, i.e.
)
2
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 Spring '11
 Shirley
 Linear Equations, Equations, F3, Gauss–Seidel method, Jacobi method, NonLinear Equations

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