LEADER 03820nam 2200661 a 450 001 9910456910903321 005 20200520144314.0 010 $a1-282-44090-X 010 $a9786612440908 010 $a981-281-183-4 035 $a(CKB)2550000000001432 035 $a(EBL)477169 035 $a(OCoLC)555793172 035 $a(SSID)ssj0000341632 035 $a(PQKBManifestationID)11226727 035 $a(PQKBTitleCode)TC0000341632 035 $a(PQKBWorkID)10396912 035 $a(PQKB)10821138 035 $a(MiAaPQ)EBC477169 035 $a(WSP)00000849 035 $a(Au-PeEL)EBL477169 035 $a(CaPaEBR)ebr10361907 035 $a(CaONFJC)MIL244090 035 $a(EXLCZ)992550000000001432 100 $a20080721d2009 uy 0 101 0 $aeng 135 $aur|n|---||||| 181 $ctxt 182 $cc 183 $acr 200 10$aPolynomial root-finding and polynomiography$b[electronic resource] /$fBahman Kalantari 210 $aSingapore ;$aHackensack, NJ $cWorld Scientific$dc2009 215 $a1 online resource (492 p.) 300 $aDescription based upon print version of record. 311 $a981-270-059-5 320 $aIncludes bibliographical references (p. 449-457) and index. 327 $aPreface; 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 327 $a10. 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 327 $a19. 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 330 $aThis 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 606 $aPolynomials 606 $aVisualization 606 $aRecurrent sequences (Mathematics) 606 $aComputer graphics 608 $aElectronic books. 615 0$aPolynomials. 615 0$aVisualization. 615 0$aRecurrent sequences (Mathematics) 615 0$aComputer graphics. 676 $a512.9/422 700 $aKalantari$b Bahman$0858091 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910456910903321 996 $aPolynomial root-finding and polynomiography$91915815 997 $aUNINA