1 QR Decomposition
Orthogonal matrix triangularization (QR decomposition) reduces a real matrix with and full rank to a much simpler form. It guarantees numerical stability by minimizing errors caused by machine roundoffs. A suitably chosen orthogonal matrix will triangularize the given matrix:
with the right triangular matrix . One only has then to solve the triangular system , where consists of the first rows of .
The least squares problem is easy to solve with and an orthogonal matrix (here and henceforth is the entire augmented matrix from above). The solution
This is a matrix-vector multiplication , followed by the solution of the triangular system by back-substitution. The QR factorization saves us the formation of and the solution of the normal equations.
- 1 The Data Analysis Briefbook. http://rkb.home.cern.ch/rkb/titleA.htmlhttp://rkb.home.cern.ch/rkb/titleA.html
|Date of creation||2013-03-22 12:06:04|
|Last modified on||2013-03-22 12:06:04|
|Last modified by||akrowne (2)|