Approximate algebraic computation: practice and problems

where IiPlI is a suitably defined norm of a polynomial P. The number ¢ is called the accuracy of operation. If we handle polynomials with floating-point number coefficients, we can calculate the result only to accuracy O(¢M), where gM is the machine epsilon. I t should be emphasized that , in the above relation, the accuracy may not be so small as O(eM) but may be as large as 10 -6 or even 10 -2. So far, we have investigated the following algebra~ic operations by implementing algorithms which we have developed. We consider these operations from the viewpoint of practical execution, by showing examples.