NEW ALGORITHM FOR MINIMIZING CHI-2 FUNCTIONALS WITH CONSTRAINTS

The problem of minimization of the functional(~)[GRAPHICS](~)with the constraints f(lambda)(X) = 0; lambda = 1 ... nc, is considered. Here: X is the vector of the parameters to be estimated, C(i)(X) = (C(X))i is the vector of functions, C(i)m are their measured values, and G-1 the covariance matrix. A new algorithm is proposed for the solution of these problems. It is based on simultaneous linearization of the functions C(i)(X) and f(lambda)(X) followed by expression of some variables in terms of others. Compared with the Lagrange multipliers method, this algorithm requires less computation and is applicable to a wider class of problems.