QR Decomposition

 

For an mxn matrix A with m>n, the QR decomposition of A is given by

 

A = Qmxn Rnxn

 

Where Q is an orthogonal matrix, and R is an upper triangular matrix.

 

In the least squares problem, Ax = b, we find Q and R via Householder transformations and solve

 

Rx = QT b