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Record Nr. |
UNINA9910781095503321 |
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Autore |
Kalantari Bahman |
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Titolo |
Polynomial root-finding and polynomiography [[electronic resource] /] / Bahman Kalantari |
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Pubbl/distr/stampa |
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Singapore ; ; Hackensack, NJ, : World Scientific, c2009 |
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ISBN |
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1-282-44090-X |
9786612440908 |
981-281-183-4 |
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Descrizione fisica |
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1 online resource (492 p.) |
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Disciplina |
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Soggetti |
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Polynomials |
Visualization |
Recurrent sequences (Mathematics) |
Computer graphics |
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Lingua di pubblicazione |
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Formato |
Materiale a stampa |
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Livello bibliografico |
Monografia |
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Note generali |
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Description based upon print version of record. |
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Nota di bibliografia |
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Includes bibliographical references (p. 449-457) and index. |
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Nota di contenuto |
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Preface; Contents; Introduction; 1. Approximation of Square-Roots and Their Visualizations; 2. The Fundamental Theorem of Algebra and a Special Case of Taylor's Theorem; 3. Introduction to the Basic Family and Polynomiography; 4. Equivalent Formulations of the Basic Family; 5. Basic Family as Dynamical System; 6. Fixed Points of the Basic Family; 7. Algebraic Derivation of the Basic Family and Characterizations; 8. The Truncated Basic Family and the Case of Halley Family; 9. Characterizations of Solutions of Homogeneous Linear Recurrence Relations |
10. Generalization of Taylor's Theorem and Newton's Method11. The Multipoint Basic Family and its Order of Convergence; 12. A Computational Study of the Multipoint Basic Family; 13. A General Determinantal Lower Bound; 14. Formulas for Approximation of Pi Based on Root-Finding Algorithms; 15. Bounds on Roots of Polynomials and Analytic Functions; 16. A Geometric Optimization and its Algebraic O springs; 17. Polynomiography: Algorithms for Visualization of Polynomial Equations; 18. Visualization of Homogeneous Linear Recurrence Relations |
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19. Applications of Polynomiography in Art, Education, Science and Mathematics20. Approximation of Square-Roots Revisited; 21. Further Applications and Extensions of the Basic Family and Polynomiography; Bibliography; Index |
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Sommario/riassunto |
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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 practi |
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