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Incomplete LU factorization - ILU

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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
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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

Revision as of 04:39, 14 September 2005

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)\inS then
e := dai,r;
ai,r := e ;
for j := (r+1) step 1 until n do
if ( (i,j)\inS ) and ( (r,j)\inS ) 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. The same algorithm could be applied to full matrix A.

Reference

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

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