Polynomial Root-finding And Polynomiography
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A01=Bahman Kalantari
Author_Bahman Kalantari
Category=PBD
Category=PBF
Category=PBKF
Category=PBW
Complex Plane
Computer Graphics
Dynamical Systems
eq_isMigrated=1
eq_isMigrated=2
eq_nobargain
Fibonacci Numbers
Numerical Analysis
Polynomial
Recurrence Relation
Root-Finding Algorithm
Visualization
Product details
- ISBN 9789812700599
- Publication Date: 09 Dec 2008
- Publisher: World Scientific Publishing Co Pte Ltd
- Publication City/Country: SG
- Product Form: Hardback
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This book offers fascinating and modern perspectives into the theory and practice of the historical subject of polynomial root-finding, rejuvenating the field via polynomiography, a creative and novel computer visualization that renders spectacular images of a polynomial equation. Polynomiography will not only pave the way for new applications of polynomials in science and mathematics, but also in art and education. The book presents a thorough development of the basic family, arguably the most fundamental family of iteration functions, deriving many surprising and novel theoretical and practical applications such as: algorithms for approximation of roots of polynomials and analytic functions, polynomiography, bounds on zeros of polynomials, formulas for the approximation of Pi, and characterizations or visualizations associated with a homogeneous linear recurrence relation. These discoveries and a set of beautiful images that provide new visions, even of the well-known polynomials and recurrences, are the makeup of a very desirable book. This book is a must for mathematicians, scientists, advanced undergraduates and graduates, but is also for anyone with an appreciation for the connections between a fantastically creative art form and its ancient mathematical foundations.
