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[null,"1.","Record Nr.",null,"UNINA9910456910903321"]
[null,null,"Autore",null,"Kalantari Bahman"]
[null,null,"Titolo",null,"Polynomial root-finding and polynomiography [[electronic resource] /] / Bahman Kalantari"]
[null,null,"Pubbl/distr/stampa",null,"Singapore ; ; Hackensack, NJ, : World Scientific, c2009"]
[null,null,"ISBN",null,"1-282-44090-X"]
[{"$nulls":4},"9786612440908"]
[{"$nulls":4},"981-281-183-4"]
[null,null,"Descrizione fisica",null,"1 online resource (492 p.)"]
[null,null,"Disciplina",null,"512.9/422"]
[null,null,"Soggetti",null,"Polynomials"]
[{"$nulls":4},"Visualization"]
[{"$nulls":4},"Recurrent sequences (Mathematics)"]
[{"$nulls":4},"Computer graphics"]
[{"$nulls":4},"Electronic books."]
[null,null,"Lingua di pubblicazione",null,"Inglese"]
[null,null,"Formato",null,"Materiale a stampa"]
[null,null,null,"Livello bibliografico","Monografia"]
[null,null,null,"Note generali","Description based upon print version of record."]
[null,null,null,"Nota di bibliografia","Includes bibliographical references (p. 449-457) and index."]
[null,null,"Nota di contenuto",null,"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"]
[{"$nulls":4},"10. Generalization of Taylor's Theorem and Newton's Method11. The Multipoint Basic Family and its Order of Convergence; 12. A Computational Study of the Multipoint Basic Family; 13. A General Determinantal Lower Bound; 14. Formulas for Approximation of Pi Based on Root-Finding Algorithms; 15. Bounds on Roots of Polynomials and Analytic Functions; 16. A Geometric Optimization and its Algebraic O springs; 17. Polynomiography: Algorithms for Visualization of Polynomial Equations; 18. Visualization of Homogeneous Linear Recurrence Relations"]
[{"$nulls":4},"19. Applications of Polynomiography in Art, Education, Science and Mathematics20. Approximation of Square-Roots Revisited; 21. Further "]
[{"$nulls":4},"Applications and Extensions of the Basic Family and Polynomiography; Bibliography; Index"]
[null,null,null,"Sommario/riassunto","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"]