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NONLINEAR LEAST SQUARES PROCEDURES

Let \( \beta^c\) denote the current parameter estimates and

S_A(beta) (approx. =) S(beta) (= by definition) sum[i=1 to n](f(x(i);beta) - y(i))^2

At each iteration:

Construct \( S_A(\beta^c) \)

Solve \( S_A(\beta^c) \) for \( \beta^+\) such that S(beta^+) < S(beta^c)

Check for convergence

If \( \beta^+\) is ``good enough''

      then stop

      else \( \beta^c\Leftarrow \beta^+\); begin next iteration