Fast and accurate computation of the euclidean norm of a vector

SUMMARY

If the true result is a floating-point number, that will be the result of the algorithms. In this note the authors will give some new algorithms for the computation of a faithfully rounding of the Euclidean norm as well as for the rounded to nearest result. The number of nearest cases improves a little bit with normExtract2, and the result of Algorithm normNearest is, of course, always rounded to nearest. The authors investigate whether the guarantee of nearest rounding causes a time penalty for Algorithm normNearest if ‖x‖ is very close to a switching point. The . . .

 



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