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GCV for Ridge Regression
It is shown in Orr (4), and stated in Orr (5, see References) that for the case of ridge regression GCV can be written as
where 
is the "effective number of parameters" that is given by
The formula for updating 
is given by
In practice, the preceding formulas are not used explicitly in Orr (5, see References). Instead a singular value decomposition of X is made, and the formulas are rewritten in terms of the eigenvalues and eigenvectors of the matrix XX'. This avoids taking the inverse of the matrix A, and it can be used to cheaply compute GCV for many values of 
.
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