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What and Who
Title:On Recent Progress in Solving Polynomial Equations - Part 1
Speaker:Michael Sagraloff
coming from:Max-Planck-Institut für Informatik - D1
Speakers Bio:
Event Type:AG1 Mittagsseminar (own work)
Visibility:D1, RG1
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Level:AG Audience
Language:English
Date, Time and Location
Date:Tuesday, 21 June 2016
Time:13:00
Duration:45 Minutes
Location:Saarbrücken
Building:E1 4
Room:024
Abstract
The computation of the roots of a univariate polynomial is one of the best studied problems in the areas of computer algebra and numerical analysis. Nevertheless, until recently, there has still been a large discrepancy between methods that are considered to be efficient in practice and those that achieve good theoretical bounds.

I will review some recently developed algorithms for real and complex root finding, which are simple and practical and whose worst-case bit complexity matches that of the best methods in theory.
Combining our techniques with a classical approach that considers so-called fractional derivatives, we can further derive a polynomial-time algorithm to compute approximations of all real roots of a sparse polynomial with arbitrary real coefficients. For very sparse polynomials with integer coefficients, the method performs near-optimal.

Contact
Name(s):Michael Sagraloff
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Created by:Michael Sagraloff, 06/08/2016 03:16 PMLast modified by:Uwe Brahm/MPII/DE, 11/24/2016 04:13 PM
  • Michael Sagraloff, 06/08/2016 03:23 PM
  • Michael Sagraloff, 06/08/2016 03:16 PM -- Created document.