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Incomplete LU factorization - ILU

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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.

Revision as of 08:12, 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

My wiki