clipper: Main Page

This is an implementation of three root finding algorithms for polynomials using geometric clipping in the Bezier representation. It was written for a lab exercise course in numerical mathematics in winter semester 2011/12 at the FernUniversity of Hagen, Germany.

For more information see the website: http://idlebox.net/2012/0320-Finding-Roots-of-Polynomials-by-Clipping/

The code implements the three algorithms BezierClip, QuadClip [1] and CubeClip [2] (both in one class KCLip) described in the referenced papers. The program follows the unusual method to printing out debug information as a LaTeX document, which itself must be compiled by pdflatex for comfortable viewing. This technique allows the algorithm code to be interleaved with ltx(...) debug lines which are can contain plots and equations.

There are six main parts in this source:

floating-point Numeric classes
polynomial classes for monomial and Bezier representation
implementation of the degree reduction matrices
the BezierClip and KClip algorithms
a test suite to check above algorithms
a collection of demos and speedtests

Each part is separately documented below (or in Related Pages).

References:

[1] Barton, M. and Juettler, B. "Computing roots of polynomials by quadratic clipping", Computer Aided Geometric Design 24, (2007) p. 125-141.

[2] Liu, L., Zhang, L., Lin, B., Wang, G. "Fast approach for computing roots of polynomials using cubic clipping", Computer Aided Geometric Design 26, (2009), p. 524-599.

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