Incomplete LU factorization - ILU - Revision history

Peter: Reverted edits by DelbaScaze (Talk) to last version by Tsaad

2008-12-19T12:38:56Z

Reverted edits by DelbaScaze (Talk) to last version by Tsaad

← Older revision		Revision as of 12:38, 19 December 2008
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-	~~letodron~~
	== Algorithm ILU ==		== Algorithm ILU ==
	Algorithm for computing ILU for a '''n''' by '''n''' matrix '''A''' is given by <br>		Algorithm for computing ILU for a '''n''' by '''n''' matrix '''A''' is given by <br>

DelbaScaze: limondarc

2008-12-19T10:13:30Z

limondarc

← Older revision		Revision as of 10:13, 19 December 2008
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		+	letodron
	== Algorithm ILU ==		== Algorithm ILU ==
	Algorithm for computing ILU for a '''n''' by '''n''' matrix '''A''' is given by <br>		Algorithm for computing ILU for a '''n''' by '''n''' matrix '''A''' is given by <br>

Tsaad: LU factorisation for sparse matrices moved to Incomplete LU factorization - ILU

2005-12-14T20:32:30Z

LU factorisation for sparse matrices moved to Incomplete LU factorization - ILU

← Older revision

Revision as of 20:32, 14 December 2005

Zxaar at 06:21, 3 October 2005

2005-10-03T06:21:55Z

← Older revision		Revision as of 06:21, 3 October 2005
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	== Reference ==		== Reference ==
	'''Tony F. Chan and Hank A. Van Der Vorst''' , "Approaximate and Incomplete Factorizations"		'''Tony F. Chan and Hank A. Van Der Vorst''' , "Approaximate and Incomplete Factorizations"
		+
		+
		+	----
		+	<i> Return to [[Numerical methods \| Numerical Methods]] </i>

Zxaar at 02:30, 15 September 2005

2005-09-15T02:30:55Z

← Older revision		Revision as of 02:30, 15 September 2005
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	== Reference ==		== Reference ==
-	''Tony F. Chan and Hank A. Van Der Vorst'' , Approaximate and Incomplete Factorizations	+	'''Tony F. Chan and Hank A. Van Der Vorst''' , "Approaximate and Incomplete Factorizations"

Zxaar at 02:30, 15 September 2005

2005-09-15T02:30:26Z

← Older revision		Revision as of 02:30, 15 September 2005
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	== Algorithm ILU ==		== Algorithm ILU ==
-	Algorithm for computing ILU for a n by n matrix A is given by <br>	+	Algorithm for computing ILU for a '''n''' by '''n''' matrix '''A''' is given by <br>
	----		----

Zxaar at 08:12, 14 September 2005

2005-09-14T08:12:32Z

← Older revision		Revision as of 08:12, 14 September 2005
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	== Algorithm ILU ==		== Algorithm ILU ==
	Algorithm for computing ILU for a n by n matrix A is given by <br>		Algorithm for computing ILU for a n by n matrix A is given by <br>
		+	----

-	for r:= 1 step 1 until n-1 do	+	: for r:= 1 step 1 until n-1 do
-	d := 1/ a<sub>rr</sub> <br>	+	:: d := 1/ a<sub>rr</sub> <br>
-	for i := (r+1) step 1 until n do <br>	+	:: for i := (r+1) step 1 until n do <br>
-	if (i,r)<math>\in</math>S then <br>	+	:: if (i,r)<math>\in</math>S then <br>
-	e := da<sub>i,r</sub>; <br>	+	::: e := da<sub>i,r</sub>; <br>
-	a<sub>i,r</sub> := e ; <br>	+	::: a<sub>i,r</sub> := e ; <br>
-	for j := (r+1) step 1 until n do <br>	+	::: for j := (r+1) step 1 until n do <br>
-	if ( (i,j)<math>\in</math>S ) and ( (r,j)<math>\in</math>S ) then <br>	+	:::: if ( (i,j)<math>\in</math>S ) and ( (r,j)<math>\in</math>S ) then <br>
-	a<sub>i,j</sub> := a<sub>i,j</sub> - e a<sub>r,j</sub> <br>	+	:::: a<sub>i,j</sub> := a<sub>i,j</sub> - e a<sub>r,j</sub> <br>
-	end if <br>	+	:::: end if <br>
-	end (j-loop) <br>	+	::: end (j-loop) <br>
-	end if <br>	+	:: end if <br>
-	end (i-loop) <br>	+	:: end (i-loop) <br>
-	end (r-loop) <br>	+	: end (r-loop) <br>
-		+	----

	Here S represents the set of elements of matrix A. The same algorithm could be applied to full matrix A.		Here S represents the set of elements of matrix A. The same algorithm could be applied to full matrix A.

Zxaar at 04:39, 14 September 2005

2005-09-14T04:39:19Z

← Older revision		Revision as of 04:39, 14 September 2005
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	== Algorithm ILU ==		== Algorithm ILU ==
-	Algorithm for computing LU for a n by n matrix A is given by <br>	+	Algorithm for computing ILU for a n by n matrix A is given by <br>

	for r:= 1 step 1 until n-1 do		for r:= 1 step 1 until n-1 do
Line 18:		Line 18:


-	Here S represents the set of elements of matrix A.	+	Here S represents the set of elements of matrix A. The same algorithm could be applied to full matrix A.

	== Reference ==		== Reference ==
	''Tony F. Chan and Hank A. Van Der Vorst'' , Approaximate and Incomplete Factorizations		''Tony F. Chan and Hank A. Van Der Vorst'' , Approaximate and Incomplete Factorizations

Zxaar at 04:38, 14 September 2005

2005-09-14T04:38:42Z

← Older revision		Revision as of 04:38, 14 September 2005
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	== Algorithm ILU ==		== Algorithm ILU ==
-	Algorithm for computing ~~ILU~~ for a n by n matrix A is given by <br>	+	Algorithm for computing LU for a n by n matrix A is given by <br>

	for r:= 1 step 1 until n-1 do		for r:= 1 step 1 until n-1 do

Zxaar at 04:34, 14 September 2005

2005-09-14T04:34:37Z

New page

== Algorithm ILU ==
Algorithm for computing ILU for a n by n matrix A is given by 

for r:= 1 step 1 until n-1 do
d := 1/ arr 
for i := (r+1) step 1 until n do 
if (i,r)<math>\in</math>S then 
e := dai,r; 
ai,r := e ; 
for j := (r+1) step 1 until n do 
if ( (i,j)<math>\in</math>S ) and ( (r,j)<math>\in</math>S ) then 
ai,j := ai,j - e ar,j 
end if 
end (j-loop) 
end if 
end (i-loop) 
end (r-loop) 

Here S represents the set of elements of matrix A.

== Reference ==
''Tony F. Chan and Hank A. Van Der Vorst'' , Approaximate and Incomplete Factorizations