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pro vyhledávání: '"George E. Collins"'
Autor:
George E. Collins
Publikováno v:
Journal of Symbolic Computation. 79:444-456
The bisection method for polynomial real root isolation was introduced by Collins and Akritas in 1976. In 1981 Mignotte introduced the polynomials A a , n ( x ) = x n - 2 ( a x - 1 ) 2 , a an integer, a ź 2 and n ź 3 . First we prove that if a is o
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::ebd99aee83b092f7346b8f15cf115bde
https://doi.org/10.1016/j.jsc.2016.02.017
https://doi.org/10.1016/j.jsc.2016.02.017
Autor:
George E. Collins
Publikováno v:
Journal of Symbolic Computation. 70:106-111
In 1879 Lagrange asserted without a proof that a certain sum of two radicals would always be an upper bound on the positive roots of any polynomial having a positive leading coefficient and at least two negative coefficients. The claim was nearly for
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::6d0ffec227e858c9997958cbd57f7831
https://doi.org/10.1016/j.jsc.2014.09.038
https://doi.org/10.1016/j.jsc.2014.09.038
Autor:
George E. Collins
This early guide is both expensive and hard to find in its first edition. A detailed description of the Brocklesby hunt foxhounds that will prove of great interest to the hunting enthusiast or historian of the sport. Extensively illustrated with blac
Autor:
George E. Collins, Werner Krandick
Publikováno v:
Journal of Symbolic Computation. 47(11):1372-1412
The maximum computing time of the continued fractions method for polynomial real root isolation is at least quintic in the degree of the input polynomial. This computing time is realized for an infinite sequence of polynomials of increasing degrees,
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https://explore.openaire.eu/search/publication?articleId=doi_dedup___::979c87cdecaa1b2e71523e7a24f2e167
Autor:
George E. Collins
Publikováno v:
Journal of Symbolic Computation. 38:1507-1521
In a 1993 paper Beauzamy, Trevisan and Wang derived a single-factor coefficient bound, one which limits the max norm (height) of at least one irreducible factor of any univariate integral polynomial A. Their bound is a function of the degree and the
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::89a751227475a69ed70397b2511ed802
https://doi.org/10.1016/j.jsc.2004.05.006
https://doi.org/10.1016/j.jsc.2004.05.006
Publikováno v:
Journal of Symbolic Computation. 34:145-157
Cylindrical algebraic decomposition requires many very time consuming operations, including resultant computation, polynomial factorization, algebraic polynomial gcd computation and polynomial real root isolation. We show how the time for algebraic p
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::695d2f94986782f2d55bd27380f0432c
https://doi.org/10.1006/jsco.2002.0547
https://doi.org/10.1006/jsco.2002.0547
Autor:
George E. Collins
Publikováno v:
Journal of Symbolic Computation. 33(4):385-392
A new version of the Euclidean algorithm is developed for computing the greatest common divisor of two Gaussian integers. It uses approximation to obtain a sequence of remainders of decreasing absolute values. The algorithm is compared with the new (
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::911630d1a7cfbb1cf6519389f350f12c
Autor:
George E. Collins, Scott M c Callum
Publikováno v:
Journal of Symbolic Computation. 33(3):321-342
We describe new algorithms for determining the adjacencies between zero-dimensional cells and those one-dimensional cells that are sections (not sectors) in cylindrical algebraic decompositions (cad). Such adjacencies constitute a basis for determini
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::b8df2a48d7bfd9428570ae2fadd25f1a
Autor:
George E. Collins
Publikováno v:
Journal of Symbolic Computation. 32:467-473
There is a well-known lower bound, due to Mignotte, for the minimum root separation of a squarefree integral polynomial, but no evidence for the sharpness of this bound. This paper provides massive computational evidence for a conjectured much larger
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::ac241d32eea03bf127883220ff2e4849
https://doi.org/10.1006/jsco.2001.0481
https://doi.org/10.1006/jsco.2001.0481
Autor:
Mark J. Encarnación, George E. Collins
Publikováno v:
Journal of Symbolic Computation. 21(3):313-327
The paper describes improved techniques for factoring univariate polynomials over the integers. The authors modify the usual linear method for lifting modular polynomial factorizations so that efficient early factor detection can be performed. The ne
Externí odkaz:
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