e wish to
are integer indexes
is the indexed family of functions. This problem originates from the described
in the previous section stochastic optimization procedure. We perform the
The last equation simplifies to the matrix
At this point we invoke the Singular Value Decomposition, see
. There exist matrices
is a square orthogonal matrix,
is a diagonal matrix and
is a matrix with orthogonal columns.
Given the fact that the minimization problem is quadratic the last expression
is the solution.
The above procedure breaks if the matrix A does not have a full rank.