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In this paper, we applied the concept of the error analysis using the linearization method and new condition numbers constituting optimal bounds in appraisals of the possible errors. Evaluations of finite continued fractions, computations of determinates of tridiagonal systems, of determinates of second order and a "fast" complex multiplication. As in Horner's scheme, present rounding error analysis of product and summation algorithms. The error estimates are tested by numerical examples. The executed program for calculation is "MATLAB 7" from the website "Mathworks.com
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