User`s guide

Cholesky Factorization
5-78
5Cholesky Factorization
Purpose Factor a square Hermitian positive definite matrix into triangular
components.
Library Math Functions / Matrices and Linear Algebra / Matrix Factorizations
Description The Cholesky Factorization block uniquely factors the square Hermitian
positive definite input matrix S as
where L is a lower triangular square matrix with positive diagonal elements
and L
*
is the Hermitian (complex conjugate) transpose of L. Only the diagonal
and upper triangle of the input matrix are used, and any imaginary component
of the diagonal entries is disregarded.
The block’s output is a composite matrix with lower triangle elements from L
and upper triangle elements from L
*
, and is always sample-based.
Note that L and L
*
share the same diagonal in the output matrix. Cholesky
factorization requires half the computation of Gaussian elimination
(LU decomposition), and is always stable.
The algorithm requires that the input be square and Hermitian positive
definite. When the input is not positive definite, the block reacts with the
behavior specified by the
Non-positive definite input parameter. The
following options are available:
•
Ignore – Proceed with the computation and do not issue an alert. The output
is not a valid factorization. A partial factorization will be present in the
upper left corner of the output.
SLL
*
=
91– 2
1– 85–
25– 7
3.00 0.33– 0.67
0.33– 2.81 1.70–
0.67 1.70– 1.91
L
3.00 0 0
0.33– 2.81 0
0.67 1.70– 1.91
=