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For the segmentation of a program it is useful to have a reasonable estimation of the values of Sij, where Sij is the mean value of the number of jumps from the ith instruction on to the ith instruction in the run time. In the cases where the Sij, are estimated directly, the structure of the whole program must be generally taken into account; therefore it is very difficult for the programmer and/or the translator to obtain a good estimation of the Sij. It is easier to estimate not Sij, but the quantities pij = Sij·ci,/∑jN=1 Sij, where c, is an arbitrary positive constant for each i. Although the pij are, for each i, proportional to Sij, the estimation of pij is easier, because we must estimate only the "probabilities" of events where instruction lj, is executed after instruction li. This estimation can often be done without considering the structure of the whole program. In the first part of the paper, using the theory of the Markov chains, an algorithm for the computation of the Sij from the p , is found, and some ways of obtaining estimates of the pij are given. In the second part a variant of this algorithm is derived, avoiding the necessity of computation involving large matrices. [ABSTRACT FROM AUTHOR]

Nonlinear least squares problems frequently arise for which the variables to be solved for can be separated into a linear and a nonlinear part. A variable projection algorithm has been developed recently which is designed to take advantage of the structure of a problem whose variables separate in this way. This paper gives a slightly more efficient and slightly more general version of this algorithm than has appeared earlier. [ABSTRACT FROM AUTHOR]