User`s guide

Cholesky Solver
5-82
5Cholesky Solver
Purpose Solve the equation SX=B for X when S is a square Hermitian positive definite
matrix.
Library Math Functions / Matrices and Linear Algebra / Linear System Solvers
Description The Cholesky Solver block solves the linear system SX=B by applying Cholesky
factorization to input matrix at the
S port, which must be square (M-by-M) and
Hermitian positive definite. Only the diagonal and upper triangle of the matrix
are used, and any imaginary component of the diagonal entries is disregarded.
The input to the
B port is the right-hand side M-by-N matrix, B. The output is
the unique solution of the equations, M-by-N matrix X, and is always
sample-based.
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 solution.
•
Warning – Proceed with the computation and display a warning message in
the MATLAB command window. The output is not a valid solution.
•
Error – Display an error dialog box and terminate the simulation.
A length-M vector input for right-hand side B is treated as an M-by-1 matrix.
Algorithm Cholesky factorization uniquely factors the Hermitian positive definite input
matrix S as
where L is a lower triangular square matrix with positive diagonal elements.
The equation SX=B then becomes
which is solved for X by making the substitution Y =L
*
X, and solving the
following two triangular systems by forward and backward substitution,
respectively.
SLL
*
=
LL
*
XB=