Nonlinear Regression and the Solution of Simultaneous Equations If one has a set of observables (Z1,...,Zm) which are bound in a relation with certain parameters (A1,...,An) by an equation S(Z1,...;A1,...)=0, one frequently has the problem of determining a set of values of the Ai which minimizes the sum of squares of differences between observed and calculated values of a distinguished observable, say Zm. If the solution of the above equation for Zm, Zm=N(Z1,...;A1,...) gives rise to a function N which is nonlinear in the Ai, then one may rely on a version of Gaussian regression [1,2] for an iteration scheme that converges to a minimizing set of values. It is shown here that this same minimization technique may be used for the solution of simultaneous (not necessarily linear) equations. CACM July, 1962 Baer, R. M. CA620725 JB March 17, 1978 8:09 PM 536 5 536 536 5 536 536 5 536