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

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