L. Petrov  "Multigroup LSQ method and its generalization"

           ABSTRACT


    Multigroup least squares method (also known as a sequential LSQ method) was
generalized into the cases of 1) two level parameter partition; 2) normal
matrices with bordered tridiagonal structure. The latter case occurs when
some parameters are modeled by linear splines. Algorithms for obtaining the
adjustments and their covariance matrices are derived. The number of
arithmetic operations is estimated as well. The number of arithmetic operations
asymptotically depends on the third degree of the number of groups of
parameters for a straightforward LSQ solution. It was shown that the number of
operations for the proposed algorithms depends linearly on the number of 
groups of parameters, which allows a dramatic decrease in computation time.