This preview shows pages 1–2. Sign up to view the full content.
Homework #5
1. Perform three iterations of Jacobi method with starting guess
~x
(0)
= [0
,
0
,
0]
t
for the
linear system
3
1

1
0

2
1
2

2
5
x
y
z
=
2
0
10
.
2. (a) Write down the ﬁxed point problem
~x
=
C~x
+
~
d
solved by Jacobi method for the
linear system of equations
±
10
1
1

1
²±
x
y
²
=
±
5

7
²
.
(b) Find the eigenvalues of
C
by hand (they are complex). Will the Jacobi method
converge in this case? Also, how does the speed of convergence compare to an
order 1 method with asympototic error constant 1
/
2?
3. Perform two iterations of the GaussSeidel method with starting guess
~x
(0)
= [0
,
0
,
0]
t
for the linear system
3
1

1
0

2
1
2

2
5
x
y
z
=
2
0
10
.
4. (a) Write down the ﬁxed point problem
~x
=
C~x
+
~
d
solved by the GaussSeidel method
for the linear system of equations
±
10
1
1

1
²±
x
y
²
=
±
5

7
²
.
(b) Find the eigenvalues of
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
This is the end of the preview. Sign up
to
access the rest of the document.
This note was uploaded on 10/17/2010 for the course MATH 174 taught by Professor Staff during the Spring '08 term at UCSD.
 Spring '08
 staff

Click to edit the document details