O'Reilly logo

Numerical Methods for Roots of Polynomials - Part II by Victor Pan, J.M. McNamee

Stay ahead with the world's most comprehensive technology and business learning platform.

With Safari, you learn the way you learn best. Get unlimited access to videos, live online training, learning paths, books, tutorials, and more.

Start Free Trial

No credit card required

15.9 Accelerated Refinement of Splitting. An Algorithm and the Error Bound

It is hard to control the precision of the computations in Algorithm 15.7.1 and their Boolean complexity for an arbitrary input of this algorithm (see Schönhage (1985) and Emiris et al. (1997)). To our advantage, however, we have a special input class, and we will achieve the desired control based on an alternative to Algorithm 15.7.1, where we will exploit the isolation properties (15.9)(15.11) for the zero sets of the factors F and G.

In this and the next two sections we will recall (and will slightly simplify by removing some contour integration techniques) such alternative algorithm from Schönhage (1982a), §11, which evaluates the polynomials and satisfying (15.40) ...

With Safari, you learn the way you learn best. Get unlimited access to videos, live online training, learning paths, books, interactive tutorials, and more.

Start Free Trial

No credit card required