Effective Topological Degree Computation Based on Interval Arithmetic
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F67985807%3A_____%2F15%3A00431141" target="_blank" >RIV/67985807:_____/15:00431141 - isvavai.cz</a>
Alternative codes found
RIV/68407700:21240/15:00240385
Result on the web
<a href="http://dx.doi.org/10.1090/S0025-5718-2014-02877-9" target="_blank" >http://dx.doi.org/10.1090/S0025-5718-2014-02877-9</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1090/S0025-5718-2014-02877-9" target="_blank" >10.1090/S0025-5718-2014-02877-9</a>
Alternative languages
Result language
angličtina
Original language name
Effective Topological Degree Computation Based on Interval Arithmetic
Original language description
We describe a new algorithm for calculating the topological degree deg (f, B, 0) where B subseteq Rn is a product of closed real intervals and f : B to Rn is a real-valued continuous function given in the form of arithmetical expressions. The algorithmcleanly separates numerical from combinatorial computation. Based on this, the numerical part provably computes only the information that is strictly necessary for the following combinatorial part, and the combinatorial part may optimize its computationbased on the numerical information computed before. We also present computational experiments based on an implementation of the algorithm. Also, in contrast to previous work, the algorithm does not assume knowledge of a Lipschitz constant of the function f, and works for arbitrary continuous functions for which some notion of interval arithmetic can be defined.
Czech name
—
Czech description
—
Classification
Type
J<sub>x</sub> - Unclassified - Peer-reviewed scientific article (Jimp, Jsc and Jost)
CEP classification
BA - General mathematics
OECD FORD branch
—
Result continuities
Project
<a href="/en/project/GCP202%2F12%2FJ060" target="_blank" >GCP202/12/J060: Integrated Verification and Falsification of Hybrid Systems of Industrial Size</a><br>
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)<br>I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace
Others
Publication year
2015
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
Mathematics of Computation
ISSN
0025-5718
e-ISSN
—
Volume of the periodical
84
Issue of the periodical within the volume
293
Country of publishing house
US - UNITED STATES
Number of pages
26
Pages from-to
1265-1290
UT code for WoS article
—
EID of the result in the Scopus database
—