# Method of Moments and Statistical Computations

## Gene Golub (Stanford University)

Many statistical computations arising in linear least squares require
the estimation of a quadratic form. We consider the problem of
determining upper and lower bounds of the quadratic form
u^{T} F(A) u
where u is a given vector, A is a symmetric positive definite matix
and F(.), an analytic function. The estimate of the quadratic form is
determined by using Gauss quadrature rules; a basic tool of our
studies is the Lanczos algorithm.
The technique we describe is useful in estimating the Generalized
Cross Validation (GCV) function and solving linear least squares with
a quadratic constraint. Our procedure is particular useful for large
data sets.