Solve *A**X*=*B* for *X* when *A* is
square matrix

Math Functions / Matrices and Linear Algebra / Linear System Solvers

`dspsolvers`

The LU Solver block solves the linear system *A**X*=*B* by
applying LU factorization to the *M*-by-*M* matrix
at the A port. The input to the B port is the right side *M*-by-*N* matrix, *B*.
The *M*-by-*N* matrix output *X* is
the unique solution of the equations.

The block treats length-*M* unoriented vector
input to the input port *B* as an *M*-by-1
matrix.

The LU algorithm factors a row-permuted variant (*A*_{p})
of the square input matrix *A* as

$${A}_{p}=LU$$

where *L* is a lower triangular square matrix
with unity diagonal elements, and *U* is an upper
triangular square matrix.

The matrix factors are substituted for *A*_{p} in

$${A}_{p}X={B}_{p}$$

where *B*_{p} is the row-permuted
variant of *B*, and the resulting equation

$$LUX={B}_{p}$$

is solved for *X* by making the substitution *Y* = *U**X*,
and solving two triangular systems.

$$\begin{array}{l}LY={B}_{p}\hfill \\ UX=Y\hfill \end{array}$$

See Solve AX=B Using the LU Solver Block in
the *DSP System Toolbox™ User's Guide*.

Double-precision floating point

Single-precision floating point

Autocorrelation LPC | DSP System Toolbox |

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LDL Solver | DSP System Toolbox |

Levinson-Durbin | DSP System Toolbox |

LU Factorization | DSP System Toolbox |

LU Inverse | DSP System Toolbox |

QR Solver | DSP System Toolbox |

See Linear System Solvers for related information.

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