When a mathematical model of a physical system is constructed, itnis often seen to contain a set of N time-invariant independent variables, xT = (x1 ... x1 ... xN). The procedure described herein enables one to find a value of x such that f(x) = 0, where f(x) is a vector of M functions defined by the system at discrete points. Once the desired behavior is attained, and if N > M, then the procedure will also optimize the system, where the criterion for this optimization is that f (x), called the payoff function, takes on an extreme value.nThe behavior of the system is approximated by a first order Taylor series in x. The resulting linear equations are solved for that Ax which produces a minimum sum-square percentage change in the variables. Once the constraints, f(x) = 0, are satisfied, the payoff function is driven to an.
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