03784nam 2200661 a 450 991082107360332120240505174012.01-282-44090-X9786612440908981-281-183-4(CKB)2550000000001432(EBL)477169(OCoLC)555793172(SSID)ssj0000341632(PQKBManifestationID)11226727(PQKBTitleCode)TC0000341632(PQKBWorkID)10396912(PQKB)10821138(MiAaPQ)EBC477169(WSP)00000849 (Au-PeEL)EBL477169(CaPaEBR)ebr10361907(CaONFJC)MIL244090(EXLCZ)99255000000000143220080721d2009 uy 0engur|n|---|||||txtccrPolynomial root-finding and polynomiography /Bahman Kalantari1st ed.Singapore ;Hackensack, NJ World Scientificc20091 online resource (492 p.)Description based upon print version of record.981-270-059-5 Includes bibliographical references (p. 449-457) and index.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 Relations10. 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 Relations19. 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; IndexThis 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 practiPolynomialsVisualizationRecurrent sequences (Mathematics)Computer graphicsPolynomials.Visualization.Recurrent sequences (Mathematics)Computer graphics.512.9/422Kalantari Bahman1692872MiAaPQMiAaPQMiAaPQBOOK9910821073603321Polynomial root-finding and polynomiography4070273UNINA