Abstract
Most numerical algorithms are designed for single or double precision floating point arithmetic, and their complexity is measured in terms of the total number of floating point operations. The resolution of problems with high condition numbers (e.g. when approaching a singularity or degeneracy) may require higher working precisions, in which case it is important to take the precision into account when doing complexity analyses. In this paper, we propose a new "ultimate complexity" model, which focuses on analyzing the cost of numerical algorithms for "sufficiently large" precisions. As an example application we will present an ultimately softly linear time algorithm for modular composition of univariate polynomials.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.