TY  - BOOK
AU  - Kalantari,Bahman
TI  - Polynomial root-finding and polynomiography
SN  - 9789812811837
AV  - QA161.P59 K35 2009eb
U1  - 512.9/422 22
PY  - 2009///
CY  - Singapore, Hackensack, NJ
PB  - World Scientific
KW  - Polynomials
KW  - Visualization
KW  - Recurrent sequences (Mathematics)
KW  - Computer graphics
KW  - Polynômes
KW  - Visualisation
KW  - Suites récurrentes (Mathématiques)
KW  - Infographie
KW  - computer graphics
KW  - aat
KW  - MATHEMATICS
KW  - Algebra
KW  - Elementary
KW  - bisacsh
KW  - fast
KW  - ram
KW  - Electronic books
N1  - Includes bibliographical references (pages 449-457) and index; Approximation of square-roots and their visualizations -- The fundamental theorem of algebra and a special case of Taylor's theorem -- Introduction to the basic family and polynomiography -- Equivalent formulations of the basic family -- Basic family as dynamical system -- Fixed points of the basic family -- Algebraic derivation of the basic family and characterizations -- The truncated basic family and the case of Halley family -- Characterizations of solutions of homogeneous linear recurrence relations -- Generalization of Taylor's theorem and Newton's method -- The multipoint basic family and its order of convergence -- A computational study of the multipoint basic family -- A general determinantal lower bound -- Formulas for approximation of pi based on root-finding algorithms -- Bounds on roots of polynomials and analytic functions -- A geometric optimization and its algebraic offsprings -- Polynomiography : algorithms for visualization of polynomial equations -- Visualization of homogeneous linear recurrence relations -- Applications of polynomiography in art, education, science, and mathematics -- Approximation of square-roots revisited -- Further applications and extensions of the basic family and polynomiography
N2  - 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
UR  - https://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&AN=305176
ER  -