QR Solver (DSP Blockset)

Find a minimum-norm-residual solution to the equation Ax=b.

Library

Linear Algebra, in Math Functions

Description

The QR Solver block solves the linear system Ax=b by applying QR factorization to the input matrix A, which can be over- or under-determined (i.e., rectangular). The bottom input is the right-hand-side of the equation, b.

The output, x, is a solution to the equations that minimizes the 2-norm of the residual b-Ax. Note that x itself is not guaranteed to be the minimum-norm solution.

QR factorization factors a column-permuted variant (A_e) of the M-by-N input matrix A as

where Q is a M-by-min(M,N) unitary matrix, and R is a min(M,N)-by-N upper-triangular matrix.

The factored matrix is substituted for A_e in

and

is solved for x by noting that Q^-1=Q^* and substituting y=Q^*b_e. This requires computing a matrix multiplication for y and solving a triangular system for x:

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

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