Matches in SemOpenAlex for { <https://semopenalex.org/work/W2242479785> ?p ?o ?g. }
- W2242479785 abstract "We describe a subdivision algorithm for isolating the complex roots of a polynomial $Finmathbb{C}[x]$. Given an oracle that provides approximations of each of the coefficients of $F$ to any absolute error bound and given an arbitrary square $mathcal{B}$ in the complex plane containing only simple roots of $F$, our algorithm returns disjoint isolating disks for the roots of $F$ in $mathcal{B}$. Our complexity analysis bounds the absolute error to which the coefficients of $F$ have to be provided, the total number of iterations, and the overall bit complexity. It further shows that the complexity of our algorithm is controlled by the geometry of the roots in a near neighborhood of the input square $mathcal{B}$, namely, the number of roots, their absolute values and pairwise distances. The number of subdivision steps is near-optimal. For the emph{benchmark problem}, namely, to isolate all the roots of a polynomial of degree $n$ with integer coefficients of bit size less than $tau$, our algorithm needs $tilde O(n^3+n^2tau)$ bit operations, which is comparable to the record bound of Pan (2002). It is the first time that such a bound has been achieved using subdivision methods, and independent of divide-and-conquer techniques such as Schonhage's splitting circle technique. Our algorithm uses the quadtree construction of Weyl (1924) with two key ingredients: using Pellet's Theorem (1881) combined with Graeffe iteration, we derive a soft-test to count the number of roots in a disk. Using Schroder's modified Newton operator combined with bisection, in a form inspired by the quadratic interval method from Abbot (2006), we achieve quadratic convergence towards root clusters. Relative to the divide-conquer algorithms, our algorithm is quite simple with the potential of being practical. This paper is self-contained: we provide pseudo-code for all subroutines used by our algorithm." @default.
- W2242479785 created "2016-06-24" @default.
- W2242479785 creator A5017265124 @default.
- W2242479785 creator A5047312965 @default.
- W2242479785 creator A5053701940 @default.
- W2242479785 creator A5078989577 @default.
- W2242479785 date "2015-09-21" @default.
- W2242479785 modified "2023-09-27" @default.
- W2242479785 title "A Near-Optimal Subdivision Algorithm for Complex Root Isolation based on the Pellet Test and Newton Iteration" @default.
- W2242479785 cites W1012836754 @default.
- W2242479785 cites W1506764403 @default.
- W2242479785 cites W1511166374 @default.
- W2242479785 cites W1518471812 @default.
- W2242479785 cites W1531175519 @default.
- W2242479785 cites W1709275931 @default.
- W2242479785 cites W1982522946 @default.
- W2242479785 cites W1983396187 @default.
- W2242479785 cites W1995250895 @default.
- W2242479785 cites W1997509004 @default.
- W2242479785 cites W2003860131 @default.
- W2242479785 cites W2015721832 @default.
- W2242479785 cites W2024560865 @default.
- W2242479785 cites W2048184489 @default.
- W2242479785 cites W2055700385 @default.
- W2242479785 cites W2059357470 @default.
- W2242479785 cites W2079536609 @default.
- W2242479785 cites W2084184830 @default.
- W2242479785 cites W2091036071 @default.
- W2242479785 cites W2097541598 @default.
- W2242479785 cites W2099287615 @default.
- W2242479785 cites W2102283069 @default.
- W2242479785 cites W2112074285 @default.
- W2242479785 cites W2112443971 @default.
- W2242479785 cites W2134534233 @default.
- W2242479785 cites W2144619406 @default.
- W2242479785 cites W2157262404 @default.
- W2242479785 cites W2168222442 @default.
- W2242479785 cites W2951710132 @default.
- W2242479785 cites W627545049 @default.
- W2242479785 cites W74955198 @default.
- W2242479785 cites W1513222260 @default.
- W2242479785 hasPublicationYear "2015" @default.
- W2242479785 type Work @default.
- W2242479785 sameAs 2242479785 @default.
- W2242479785 citedByCount "0" @default.
- W2242479785 crossrefType "posted-content" @default.
- W2242479785 hasAuthorship W2242479785A5017265124 @default.
- W2242479785 hasAuthorship W2242479785A5047312965 @default.
- W2242479785 hasAuthorship W2242479785A5053701940 @default.
- W2242479785 hasAuthorship W2242479785A5078989577 @default.
- W2242479785 hasConcept C101044782 @default.
- W2242479785 hasConcept C107775665 @default.
- W2242479785 hasConcept C11413529 @default.
- W2242479785 hasConcept C114614502 @default.
- W2242479785 hasConcept C11577676 @default.
- W2242479785 hasConcept C118615104 @default.
- W2242479785 hasConcept C121332964 @default.
- W2242479785 hasConcept C134306372 @default.
- W2242479785 hasConcept C138885662 @default.
- W2242479785 hasConcept C143392562 @default.
- W2242479785 hasConcept C158622935 @default.
- W2242479785 hasConcept C166957645 @default.
- W2242479785 hasConcept C194777461 @default.
- W2242479785 hasConcept C199360897 @default.
- W2242479785 hasConcept C2524010 @default.
- W2242479785 hasConcept C2780388253 @default.
- W2242479785 hasConcept C33923547 @default.
- W2242479785 hasConcept C41008148 @default.
- W2242479785 hasConcept C41895202 @default.
- W2242479785 hasConcept C45340560 @default.
- W2242479785 hasConcept C62520636 @default.
- W2242479785 hasConcept C77553402 @default.
- W2242479785 hasConcept C90119067 @default.
- W2242479785 hasConcept C95457728 @default.
- W2242479785 hasConcept C97137487 @default.
- W2242479785 hasConceptScore W2242479785C101044782 @default.
- W2242479785 hasConceptScore W2242479785C107775665 @default.
- W2242479785 hasConceptScore W2242479785C11413529 @default.
- W2242479785 hasConceptScore W2242479785C114614502 @default.
- W2242479785 hasConceptScore W2242479785C11577676 @default.
- W2242479785 hasConceptScore W2242479785C118615104 @default.
- W2242479785 hasConceptScore W2242479785C121332964 @default.
- W2242479785 hasConceptScore W2242479785C134306372 @default.
- W2242479785 hasConceptScore W2242479785C138885662 @default.
- W2242479785 hasConceptScore W2242479785C143392562 @default.
- W2242479785 hasConceptScore W2242479785C158622935 @default.
- W2242479785 hasConceptScore W2242479785C166957645 @default.
- W2242479785 hasConceptScore W2242479785C194777461 @default.
- W2242479785 hasConceptScore W2242479785C199360897 @default.
- W2242479785 hasConceptScore W2242479785C2524010 @default.
- W2242479785 hasConceptScore W2242479785C2780388253 @default.
- W2242479785 hasConceptScore W2242479785C33923547 @default.
- W2242479785 hasConceptScore W2242479785C41008148 @default.
- W2242479785 hasConceptScore W2242479785C41895202 @default.
- W2242479785 hasConceptScore W2242479785C45340560 @default.
- W2242479785 hasConceptScore W2242479785C62520636 @default.
- W2242479785 hasConceptScore W2242479785C77553402 @default.
- W2242479785 hasConceptScore W2242479785C90119067 @default.
- W2242479785 hasConceptScore W2242479785C95457728 @default.
- W2242479785 hasConceptScore W2242479785C97137487 @default.