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Computing Real Roots of Real Polynomials and its Application in Computational Geometry
Published on May 04, 20153157 Views
I also discuss recent advances in the computation of real roots of real polynomials. Near optimal solutions for the more general problem of isolating the complex roots of complex polynomials are know
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Chapter list
Determining the Real Roots of Real Polynomials00:00
Overview03:28
The Real Root Isolation Problem05:06
Motivation: Nonlinear Computational Geometry06:27
Motivation07:15
A Glimpse at the Arrangement Computation07:28
The State of the Art10:21
A Hard Example: Mignotte Polynomials13:59
The Descartes Method for Real Root Isolation18:17
Number of Sign Changes19:04
Descartes Method23:57
Analysis of Descartes Method26:09
Two Questions29:18
Analysis of Descartes Method Revisited30:50
Algorithm ANewDsc35:23
Bitstream Coefficients35:34
Sign Variations in Sequences of Intervals37:24
A First Idea: Eigenwillig/Kettner/Krandick/KM/Schmitt/Wolpert (05)39:27
Interval Descartes Method43:19
Second Idea: Sagraloff (2014)44:25
Clusters of roots (a bit of wishful thinking)45:17
Clusters of roots: The situation - 149:27
Clusters of roots: The situation - 252:26
Clusters of roots: The situation - 353:30
Summary56:02