Algorithms for Polynomial Real Root Isolation

Texts and Monographs in Symbolic Computation - Quantifier Elimination and Cylindrical Algebraic Decomposition ◽

10.1007/978-3-7091-9459-1_13 ◽

1998 ◽

pp. 269-299 ◽

Cited By ~ 10

Author(s):

J. R. Johnson

Keyword(s):

Real Root ◽

Root Isolation ◽

Polynomial Real Root Isolation ◽

Real Root Isolation

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Polynomial real root isolation by differentiation

10.1145/800205.806319 ◽

1976 ◽

Cited By ~ 16

Author(s):

George E. Collins ◽

Rüdiger Loos

Keyword(s):

Real Root ◽

Root Isolation ◽

Polynomial Real Root Isolation ◽

Real Root Isolation

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A short note on a new method for polynomial real root isolation

ACM SIGSAM Bulletin ◽

10.1145/1088276.1088277 ◽

1978 ◽

Vol 12 (4) ◽

pp. 12-13 ◽

Cited By ~ 2

Author(s):

Alkiviadis G. Akritas

Keyword(s):

Real Root ◽

Short Note ◽

New Method ◽

Root Isolation ◽

Polynomial Real Root Isolation ◽

Real Root Isolation

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Polynomial Real Root Isolation by Means of Root Radii Approximation

Computer Algebra in Scientific Computing - Lecture Notes in Computer Science ◽

10.1007/978-3-319-24021-3_26 ◽

2015 ◽

pp. 349-360 ◽

Cited By ~ 3

Author(s):

Victor Y. Pan ◽

Liang Zhao

Keyword(s):

Real Root ◽

Root Isolation ◽

Polynomial Real Root Isolation ◽

Real Root Isolation

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Polynomial real root isolation using approximate arithmetic

Proceedings of the 1997 international symposium on Symbolic and algebraic computation - ISSAC '97 ◽

10.1145/258726.258790 ◽

1997 ◽

Cited By ~ 9

Author(s):

J. R. Johnson ◽

Werner Krandick

Keyword(s):

Real Root ◽

Root Isolation ◽

Polynomial Real Root Isolation ◽

Real Root Isolation

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Univariate Polynomial Real Root Isolation: Continued Fractions Revisited

Lecture Notes in Computer Science - Algorithms – ESA 2006 ◽

10.1007/11841036_72 ◽

2006 ◽

pp. 817-828 ◽

Cited By ~ 9

Author(s):

Elias P. Tsigaridas ◽

Ioannis Z. Emiris

Keyword(s):

Continued Fractions ◽

Real Root ◽

Root Isolation ◽

Univariate Polynomial ◽

Polynomial Real Root Isolation ◽

Real Root Isolation

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A new method for polynomial real root isolation

10.1145/503643.503653 ◽

1978 ◽

Cited By ~ 6

Author(s):

Alkiviadis G. Akritas

Keyword(s):

Real Root ◽

New Method ◽

Root Isolation ◽

Polynomial Real Root Isolation ◽

Real Root Isolation

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Polynomial real root isolation using Descarte's rule of signs

10.1145/800205.806346 ◽

1976 ◽

Cited By ~ 61

Author(s):

George E. Collins ◽

Alkiviadis G. Akritas

Keyword(s):

Real Root ◽

Root Isolation ◽

Polynomial Real Root Isolation ◽

Real Root Isolation

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Real root isolation for exp-log functions

Proceedings of the twenty-first international symposium on Symbolic and algebraic computation - ISSAC '08 ◽

10.1145/1390768.1390810 ◽

2008 ◽

Cited By ~ 7

Author(s):

Adam Strzebonski

Keyword(s):

Real Root ◽

Root Isolation ◽

Real Root Isolation

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Parallel Real Root Isolation Using the Descartes Method

Lecture Notes in Computer Science - High Performance Computing – HiPC’99 ◽

10.1007/978-3-540-46642-0_38 ◽

1999 ◽

pp. 261-268 ◽

Cited By ~ 5

Author(s):

Thomas Decker ◽

Werner Krandick

Keyword(s):

Real Root ◽

Root Isolation ◽

Real Root Isolation

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Dynamics of a Prey–Predator System with Foraging Facilitation in Predators

International Journal of Bifurcation and Chaos ◽

10.1142/s0218127420500091 ◽

2020 ◽

Vol 30 (01) ◽

pp. 2050009

Author(s):

Yong Yao

Keyword(s):

Numerical Simulations ◽

Real Root ◽

Qualitative Properties ◽

Isolation Technique ◽

Root Isolation ◽

Number Of Equilibria ◽

Complete Investigation ◽

Theoretical Results ◽

Predator System ◽

Real Root Isolation

The dynamics of a prey–predator system with foraging facilitation among predators are investigated. The analysis involves the computation of many semi-algebraic systems of large degrees. We apply the pseudo-division reduction, real-root isolation technique and complete discrimination system of polynomial to obtain the parameter conditions for the exact number of equilibria and their qualitative properties as well as do a complete investigation of bifurcations including saddle-node, transcritical, pitchfork, Hopf and Bogdanov–Takens bifurcations. Moreover, numerical simulations are presented to support our theoretical results.

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