Incomplete Cholesky factorization
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=== Algorithm for full matrix ''A'' === | === Algorithm for full matrix ''A'' === | ||
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We have by definition | We have by definition | ||
<math> | <math> | ||
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From this we can easily obtain<br> | From this we can easily obtain<br> | ||
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'''for := 1 step 1 until N do''' <br> | '''for := 1 step 1 until N do''' <br> | ||
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'''end (i-loop)''' <br> | '''end (i-loop)''' <br> | ||
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Revision as of 12:32, 14 September 2005
Cholesky Factorization
When the square matrix A is symmetric and positive definite then it has an efficient triangular decomposition. Symmetric means that aij = aji for i,j = 1, ... , N. While positive definite means that
In cholesky factorization we construct a lower triangular matrix L whose transpose LT can itself serve as upper triangular part.
In other words we have
L 
LT = A
Algorithm for full matrix A
We have by definition
From this we can easily obtain
for := 1 step 1 until N do
and
; where j = i+1, i+2, ..., N
end (i-loop)
