It can be solved by Choleski methods. However, internally the matrix is converted to a real form. Although this has an, in general, small memory penalty, it has no influence on CPU time, and makes it possible to use the same routines for complex and real solutions. Another reason for solving real rather than complex equations is given in the next section. We could, of course, solve for 2 n complex equations with added constraints that the sum of even and odd unknowns must be real, and their difference imaginary, but this will lead to 4 n complex equations.
Several implementations exist in the literature.
The general constraint situation arises from the use of Lagrange multiplicators. Note that I have chosen for having constraint equations linear in the unknowns, with a zero value. I will briefly describe Hans' paper, together with the additions I have made. In the case we are considering, the normal equation A has not full column rank. Do a Cholesky factorisation of the normal equations A until the remaining columns of A are dependent.