Interval Projected Polyhedron (IPP) Algorithm Overview
Subdivision Method using the Multivariate Bernstein Basis.
- Conversion to a geometric problem for use of the convex hull property.
Rounded Interval Arithmetic (RIA)
- Robust computation with hardware rounding.
Algorithm
- Problem formulation using exact arithmetic or RIA, affine parameter transformation and the linear precision property.
- Convex hull property : eliminate regions which do not contain root(s).
- Subdivision : de Casteljau algorithm in RIA.
Asymptotic Time Complexity Per Step. O(nlml+1)
- m : Degree in each variable.
- n : Number of equations.
- l : Number of variables ( n need not be equal to l ).