Normal equations for linear least squares problems

The objective is to find the value of tex2html_wrap_inline147 that minimizes

displaymath149

This can be solved by finding the derivative of the objective function with respect to tex2html_wrap_inline147 , setting equal to zero and solving the resulting system of linear equations.

Differentiating with respect to tex2html_wrap_inline153 gives

displaymath155

This is better expressed in matrix notation as

displaymath157

where R is the residual vector (nothing to do with the Q-R decomposition!), the Normal Equations.


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Next: A non-linear least squares Up: Class 5 Stat 540 Previous: Review of QR algorithm

Richard Waterman
Fri Feb 12 06:43:38 EST 1999