This letter presents a new fast QR algorithm based on Givens rotations
using a priori errors, The principles behind the triangularization of
the weighted input data matrix via QR decomposition and the type of e
rrors used in the updating process are exploited in order to investiga
te the relationships among different fast algorithms of the QR family,
These algorithms are classified according to a general framework and
a detailed description of the new algorithm is presented.