QR Solver
Find minimumnormresidual solution to AX=B
Libraries:
DSP System Toolbox /
Math Functions /
Matrices and Linear Algebra /
Linear System Solvers
Description
The QR Solver block solves the linear system AX=B, which can be overdetermined, underdetermined, or exactly determined. The block applies QR factorization to the matrix A to find the minimumnormresidual solution to AX=B. For more details, see Algorithms.
Ports
Input
Output
Parameters
Block Characteristics
Data Types 

Direct Feedthrough 

Multidimensional Signals 

VariableSize Signals 

ZeroCrossing Detection 

Algorithms
QR factorization factors a columnpermuted variant (A_{e}) of the MbyN input matrix A as
A_{e} = QR
where Q is a
Mbymin
(M,N)
unitary matrix, and R is a
min
(M,N)byN
uppertriangular matrix.
The factored matrix is substituted for A_{e} in
A_{e}X = B_{e}
and
QRX = B_{e}
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.
RX = Y
Extended Capabilities
Version History
Introduced before R2006a