| This class represents the decomposition of a
Matrix matrix
A into a product of a
LUDecomposition.getLower lower
and
LUDecomposition.getUpper upper triangular matrices, L
and U respectively, such as A = P·L·U with
P a
LUDecomposition.getPermutation permutation matrix.
This decomposition is typically used to resolve linear systems
of equations (Gaussian elimination) or to calculate the determinant
of a square
Matrix (O(m³)).
Numerical stability is guaranteed through pivoting if the
Field elements are
Number numbers For others elements types, numerical stability can be ensured by setting
the
javolution.context.LocalContext context-local pivot
comparator (see
LUDecomposition.setPivotComparator ).
Pivoting can be disabled by setting the
LUDecomposition.setPivotComparator pivot comparator to null (
LUDecomposition.getPermutation P
is then the matrix identity).
author:
Jean-Marie Dautelle
version:
3.3, January 2, 2007
See Also:
* Wikipedia: LU decomposition | 