Numerical stability of Newton's algorithm applied to minimization of (chi)(sup 2) functionals is considered. It is shown that the increase of experimental data precision leads to growth of numerical instability of this algorithm as well as of its modifications. As one of possible ways to suppress these instabilities 'semi-analytical' algorithm of (chi)(sup 2) derivatives calculation is investigated. It is shown that application of the algorithm can save at least one order of magnitude of the required calculation precision of theoretical expectation in Z-boson line shape fitting. 3 refs., 3 figs., 1 tab. (Atomindex citation 26:048058)
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