Numerical certification: Difference between revisions

Revision as of 14:01, 3 May 2019

Revision as of 08:49, 9 August 2019

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<math display="block">\left\|N^k(x)-x^\ast\right\|\leq\frac{1}{2^{2^k-1}}\|x-x^\ast\|.</math>

The software package [http://www.math.tamu.edu/~sottile/research/stories/alphaCertified/ alphaCertified] provides an implementation of the alpha test for polynomials by estimating <math>\beta</math> and <math>\gamma</math>.<ref name="alphacertified">{{cite journal |last1=Hauenstein |first1=Jonathan |last2=Sottile |first2=Frank |title=Algorithm 921: alphaCertified: certifying solutions to polynomial systems |journal=ACM Transactions on Mathematical Software (TOMS) |date=2012 |volume=38 |issue=4 |page=28 |doi=10.1145/2331130.2331136}}</ref>

=== Interval Newton and Krawczyck Methods ===