Polynomial root-finding and polynomiography

Research output: Book/ReportBook

52 Citations (Scopus)

Abstract

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.

Original languageEnglish (US)
PublisherWorld Scientific Publishing Co.
Number of pages467
ISBN (Electronic)9789812811837
ISBN (Print)9789812700599
DOIs
StatePublished - Jan 1 2008

Fingerprint

Polynomial Roots
Root-finding
Visualization
Linear Recurrence Relation
Iteration Function
Zeros of Polynomials
Polynomial
Polynomial equation
Approximation
Polynomial function
Pi
Recurrence
Analytic function
Roots
Family
Art

All Science Journal Classification (ASJC) codes

  • Mathematics(all)

Cite this

Kalantari, Bahman. / Polynomial root-finding and polynomiography. World Scientific Publishing Co., 2008. 467 p.
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Polynomial root-finding and polynomiography. / Kalantari, Bahman.

World Scientific Publishing Co., 2008. 467 p.

Research output: Book/ReportBook

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