On the quality of some root-bounds

Publikationstyp
Conference Paper
Date Issued
2016
Sprache
English
Author(s)
Batra, Prashant  orcid-logo
Institut
Zuverlässiges Rechnen E-19  
TORE-URI
http://hdl.handle.net/11420/6290
First published in
Lecture notes in computer science  
Number in series
9582 LNCS
Start Page
591
End Page
595
Citation
Lecture Notes in Computer Science (9582): 591-595 (2016)
Publisher DOI
10.1007/978-3-319-32859-1_50
Scopus ID
2-s2.0-84964038701
Publisher
Springer
Bounds for the maximum modulus of all positive (or all complex) roots of a polynomial are a fundamental building block of algorithms involving algebraic equations. We apply known results to show which are the salient features of the Lagrange (real) root-bound as well as the related bound by Fujiwara. For a polynomial of degree n, we construct a bound of relative overestimation at most 1.72n which overestimates the Cauchy root by a factor of two at most. This can be carried over to the bounds by Kioustelidis and Hong. Giving a very short variant of a recent proof presented by Collins, we sketch a way to further definite, measurable improvement.
Subjects
Improvements of Lagrange’s bound
Maximum modulus of polynomial roots
Maximum overestimation
DDC Class
004: Informatik