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D.8.8 rootisolation_lib
- Library:
- rootisolation.lib
- Purpose:
- implements an algorithm for real root isolation
using interval arithmetic
- Authors:
- Dominik Bendle (bendle@rhrk.uni-kl.de)
Janko Boehm (boehm@mathematik.uni-lk.de), supervisor Fachpraktikum
Clara Petroll (petroll@rhrk.uni-kl.de)
- Overview:
- In this library the interval arithmetic from
interval.so
is used. The new type ivmat , a matrix consisting of
intervals, is implemented as newstruct . There are various
functions for computations with interval matrices implemented, such
as Gaussian elimination for interval matrices.
Interval arithmetic, the interval Newton Step and exclusion methods
are used to implement the procedure rootIsolation , an
algorithm which finds boxes containing elements of the vanishing
locus of an ideal. This algorithm is specialised for
zero-dimensional radical ideals. The theory about the interval
Newton Step is detailed in [2].
Note that interval arithmetic and the aforementioned procedures are
intended for rational or real polynomial rings.
- References:
- [1] Cloud, Kearfott, Moore: Introduction to Interval Analysis,
Society for Industrial and Applied Mathematics, 2009
[2] Eisenbud, Grayson, Herzog, Stillman, Vasconcelos: Computational
Methods in Commutative Algebra and Algebraic Geometry, Springer
Verlag Berlin-Heidelberg, 3. edition 2004
[3] Andrew J. Sommese and Charles W. Wampler: The Numerical
Solution of Systems of Polynomials - Arising in Engineering and
Science, World Scientific Publishing Co. Pte. Ltd., 2005
- Overloads:
- [ ivmatGet indexing
print ivmatPrint printing
nrows ivmatNrows number of rows
ncols ivmatNcols number of columns
* ivmatMultiplyGeneral matrix multiplication
Procedures:
See also:
interval_lib.
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