LU Solver
Solve AX = B when A is a square matrix
Libraries:
DSP System Toolbox /
Math Functions /
Matrices and Linear Algebra /
Linear System Solvers
Description
The LU Solver block solves the linear system AX = B by applying LU factorization, where:
A is an MbyM square matrix input through the A port.
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
Block Characteristics
Data Types 

Direct Feedthrough 

Multidimensional Signals 

VariableSize Signals 

ZeroCrossing Detection 

Algorithms
The LU algorithm factors a rowpermuted 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 rowpermuted variant of B, and the resulting equation
$$LUX={B}_{p}$$
is solved for X by substituting Y = UX, and solving two triangular systems.
$$\begin{array}{l}LY={B}_{p}\hfill \\ UX=Y\hfill \end{array}$$
Extended Capabilities
Version History
Introduced before R2006a
See Also
Autocorrelation LPC  Cholesky Solver  LDL Solver  LevinsonDurbin  LU Factorization  LU Inverse  QR Solver