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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...
| Clasificación: | Libro Electrónico |
|---|---|
| Autor principal: | |
| Formato: | Electrónico eBook |
| Idioma: | Inglés |
| Publicado: |
Singapore ; Hackensack, NJ :
World Scientific,
©2009.
|
| Temas: | |
| Acceso en línea: | Texto completo |
MARC
| LEADER | 00000cam a2200000Ia 4500 | ||
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| 020 | |z 9812700595 |q (hardcover ; |q alk. paper) | ||
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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 | ||
| 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 | |
| 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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