# Incomplete LU factorization - ILU

(Difference between revisions)
 Revision as of 04:39, 14 September 2005 (view source)Zxaar (Talk | contribs)← Older edit Latest revision as of 12:38, 19 December 2008 (view source)Peter (Talk | contribs) m (Reverted edits by DelbaScaze (Talk) to last version by Tsaad) (6 intermediate revisions not shown) Line 1: Line 1: == Algorithm ILU == == Algorithm ILU == - Algorithm for computing ILU for a n by n matrix A is given by
+ 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)$\in$S then
+ - e := dai,r;
+ - ai,r := e ;
+ - for j := (r+1) step 1 until n do
+ - if ( (i,j)$\in$S ) and ( (r,j)$\in$S ) then
+ - ai,j := ai,j - e ar,j
+ - end if
+ - end (j-loop)
+ - end if
+ - end (i-loop)
+ - end (r-loop)
+ + :  for r:= 1 step 1 until n-1 do + ::      d := 1/ arr
+ ::      for i := (r+1) step 1 until n do
+ ::          if (i,r)$\in$S then
+ :::            e := dai,r;
+ :::            ai,r := e ;
+ :::            for j := (r+1) step 1 until n do
+ ::::              if ( (i,j)$\in$S ) and ( (r,j)$\in$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. 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. == 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" + + + ---- + Return to [[Numerical methods | Numerical Methods]]

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

## Reference

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