LU Solver (DSP Blockset)

Solve the equation Ax=b for square matrix A.

Library

Linear Algebra, in Math Functions

Description

The LU Solver block solves the linear system Ax=b by applying LU factorization to matrix A (top input), which must be square. The bottom input is the right-hand-side of the equation, b. The output is the unique solution of the equations, x.

LU factorization factors a row-permuted variant (A_p) 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 A_p in

where b_p 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:

The block may generate NaN or Inf for underdetermined or inconsistent (overdetermined) systems.

Dialog Box