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Polynomial root-finding and polynomiography /

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 wi...

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Detalles Bibliográficos
Clasificación:Libro Electrónico
Autor principal: Kalantari, Bahman
Formato: Electrónico eBook
Idioma:Inglés
Publicado: Singapore ; Hackensack, NJ : World Scientific, ©2009.
Temas:
Acceso en línea:Texto completo

MARC

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100 1 |a Kalantari, Bahman. 
245 1 0 |a Polynomial root-finding and polynomiography /  |c Bahman Kalantari. 
260 |a Singapore ;  |a Hackensack, NJ :  |b World Scientific,  |c ©2009. 
300 |a 1 online resource (xxiii, 467 pages) :  |b illustrations (some color) 
336 |a text  |b txt  |2 rdacontent 
337 |a computer  |b c  |2 rdamedia 
338 |a online resource  |b cr  |2 rdacarrier 
504 |a Includes bibliographical references (pages 449-457) and index. 
505 0 |a 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. 
588 0 |a Print version record. 
520 |a 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. 
590 |a eBooks on EBSCOhost  |b EBSCO eBook Subscription Academic Collection - Worldwide 
590 |a ProQuest Ebook Central  |b Ebook Central Academic Complete 
650 0 |a Polynomials. 
650 0 |a Visualization. 
650 0 |a Recurrent sequences (Mathematics) 
650 0 |a Computer graphics. 
650 6 |a Polynômes. 
650 6 |a Visualisation. 
650 6 |a Suites récurrentes (Mathématiques) 
650 6 |a Infographie. 
650 7 |a computer graphics.  |2 aat 
650 7 |a MATHEMATICS  |x Algebra  |x Elementary.  |2 bisacsh 
650 7 |a Computer graphics  |2 fast 
650 7 |a Polynomials  |2 fast 
650 7 |a Recurrent sequences (Mathematics)  |2 fast 
650 7 |a Visualization  |2 fast 
650 7 |a Visualisation.  |2 ram 
650 7 |a Polynômes.  |2 ram 
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776 0 8 |i Print version:  |a Kalantari, Bahman.  |t Polynomial root-finding and polynomiography.  |d Singapore ; Hackensack, NJ : World Scientific, ©2009  |z 9789812700599  |w (DLC) 2008032272  |w (OCoLC)235946095 
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