Cholesky Solver
Solve SX = B for X when S is a square Hermitian positive definite matrix
Libraries:
DSP System Toolbox /
Math Functions /
Matrices and Linear Algebra /
Linear System Solvers
Description
The Cholesky Solver block solves the linear system SX = B by applying the Cholesky factorization to the input matrix, where:
S is an MbyM square matrix input through the S port. The matrix must be Hermitian positive definite.
B is an MbyN matrix input through the B port.
X is the MbyN output matrix and is the unique solution to the equations.
Ports
Input
Output
Parameters
Block Characteristics
Data Types 

Direct Feedthrough 

Multidimensional Signals 

VariableSize Signals 

ZeroCrossing Detection 

Algorithms
Cholesky factorization uniquely factors the Hermitian positive definite input matrix S as
$$S=L{L}^{\ast}$$
where L is a lower triangular square matrix with positive diagonal elements.
The equation SX = B then becomes
$$L{L}^{\ast}X=B,$$
which is solved for X by substituting $$Y={L}^{\ast}X$$ and solving the following two triangular systems by forward and backward substitution, respectively.
$$LY=B$$
$${L}^{\ast}X=Y$$
Extended Capabilities
Version History
Introduced before R2006a
See Also
Blocks
 Autocorrelation LPC  Cholesky Factorization  Cholesky Inverse  LDL Solver  LU Solver  QR Solver