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LU Solver

Solve AX=B for X when A is square matrix


Math Functions / Matrices and Linear Algebra / Linear System Solvers



The LU Solver block solves the linear system AX=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 (Ap) of the square input matrix A as


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 Ap in


where Bp is the row-permuted variant of B, and the resulting equation


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



See Linear System Solvers for an example that uses the LU Solver block.

Supported Data Types

  • Double-precision floating point

  • Single-precision floating point

See Also

Autocorrelation LPCDSP System Toolbox
Cholesky SolverDSP System Toolbox
LDL SolverDSP System Toolbox
Levinson-DurbinDSP System Toolbox
LU FactorizationDSP System Toolbox
LU InverseDSP System Toolbox
QR SolverDSP System Toolbox

See Linear System Solvers for related information.

Introduced before R2006a

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