Skip to content
GitLab
Menu
Projects
Groups
Snippets
Help
Help
Support
Community forum
Keyboard shortcuts
?
Submit feedback
Contribute to GitLab
Sign in
Toggle navigation
Menu
Open sidebar
Jaap, Patrick
skript-mehrgitter
Commits
d5512f7e
Commit
d5512f7e
authored
Apr 15, 2021
by
Jaap, Patrick
Browse files
Index i<->j im Jacobiverfahren korrigiert
parent
46faca62
Pipeline
#6200
passed with stage
in 3 minutes and 25 seconds
Changes
1
Pipelines
1
Hide whitespace changes
Inline
Side-by-side
skript-mehrgitter-sander.tex
View file @
d5512f7e
...
...
@@ -674,9 +674,9 @@ Für $i=1,\ldots,n$
\begin{equation*}
x
_
i
^{
k+1
}
=
\frac
{
1
}{
A
_{
ii
}}
\bigg
(b
_
i-
\sum
_{
\substack
{
j=1
\\
j
\neq
i
}}^
n A
_{
ij
}
x
_
i
^
k
\bigg
)
\frac
{
1
}{
A
_{
ii
}}
\bigg
(b
_
i-
\sum
_{
\substack
{
j=1
\\
j
\neq
i
}}^
n A
_{
ij
}
x
_
j
^
k
\bigg
)
=
x
^
k
_
i +
\frac
{
1
}{
A
_{
ii
}}
\bigg
(b
_
i-
\sum
_{
j=1
}^
n A
_{
ij
}
x
_
i
^
k
\bigg
).
x
^
k
_
i +
\frac
{
1
}{
A
_{
ii
}}
\bigg
(b
_
i-
\sum
_{
j=1
}^
n A
_{
ij
}
x
_
j
^
k
\bigg
).
\end{equation*}
Beachte:
\begin{itemize}
...
...
@@ -695,7 +695,7 @@ Dabei wählt man einen Parameter $\eta > 0$ und definiert
\begin{equation*}
x
_
i
^{
k+1
}
=
x
^
k
_
i +
\frac
{
\eta
}{
A
_{
ii
}}
\bigg
(b
_
i-
\sum
_{
j=1
}^
n A
_{
ij
}
x
_
i
^
k
\bigg
)
x
^
k
_
i +
\frac
{
\eta
}{
A
_{
ii
}}
\bigg
(b
_
i-
\sum
_{
j=1
}^
n A
_{
ij
}
x
_
j
^
k
\bigg
)
\qquad
\text
{
bzw.
}
\qquad
x
^{
k+1
}
= x
^
k +
\eta
D
^{
-1
}
( b - Ax
^
k).
\end{equation*}
...
...
Write
Preview
Supports
Markdown
0%
Try again
or
attach a new file
.
Attach a file
Cancel
You are about to add
0
people
to the discussion. Proceed with caution.
Finish editing this message first!
Cancel
Please
register
or
sign in
to comment