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Solve *S*X=*B* for X
when *S* is square Hermitian positive definite matrix

The Cholesky Solver block solves the linear system *S*X=*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 side *M*-by-*N* matrix, *B*.
The *M*-by-*N* output matrix X is
the unique solution of the equations.

A length-*M* vector input for right side *B* is
treated as an *M*-by-1 matrix.

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.

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 , and solving the following two triangular systems by forward and backward substitution, respectively.

**Non-positive definite input**Response to nonpositive definite matrix inputs:

`Ignore`,`Warning`, or`Error`. See Response to Nonpositive Definite Input.

Autocorrelation LPC | DSP System Toolbox |

Cholesky Factorization | DSP System Toolbox |

Cholesky Inverse | DSP System Toolbox |

LDL Solver | DSP System Toolbox |

LU Solver | DSP System Toolbox |

QR Solver | DSP System Toolbox |

chol | MATLAB |

See Linear System Solvers for related information.

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