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7. Literatur

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  1. Liang Fang, Lili Ni, Rui Chen: ThreeModified EfficientIterativeMethodsfor Non-linear Equations
  2. Mohamed S.M. Bahgat, M.A. Hafiz: THREE-STEP ITERATIVE METHOD WITH EIGHTEENTH ORDER CONVERGENCE FOR SOLVING NONLINEAR EQUATIONS
  3. Namir Shammas: Ostrowski’s Method for Finding Roots
  4. Gregory Louis Zitelli: Fractals from root finding algorithms
  5. "Numerical methods for roots of polynomials. Part I" by John M. McNamee
  6. Rajinder Thukral: Eighth-Order Iterative Methods without Derivatives for Solving Nonlinear Equations
  7. JUAN L. VARONA: GRAPHIC AND NUMERICAL COMPARISON BETWEEN ITERATIVE METHODS
  8. Nils B. Lahr: Visualizing Newton's Method on Fractional Exponents
  9. Young Ik Kim: A FOURTH-ORDER FAMILY OF TRIPARAMETRIC EXTENSIONS OF JARRATT'S METHOD
  10. M. Fardi, M. Ghasemi, A. Davari: New Iterative Methods With Seventh-Order Convergence For Solving Nonlinear Equations
  11. Dr. Vinay Kumar, Prof. C. P. Katti: On high order methods for solution of non-linear equation
  12. Nikolay Kyurkchiev, Anton Iliev: A NOTE ON THE “CONSTRUCTING” OF NONSTATIONARY METHODS FOR SOLVING NONLINEAR EQUATIONS WITH RAISED SPEED OF CONVERGENCE.
  13. Osama Yusuf Ababneh: New Newton’s Method with Third-order Convergence for Solving Nonlinear Equations
  14. Bijan Rahimi, Behzad Ghanbari and Mehdi Gholami Porshokouhi: Some Third-Order Modifications of Newton’s Method
  15. M.A. Hafiz, Salwa M. H. Al-Goria: NEW NINTH– AND SEVENTH–ORDER METHODS FOR SOLVING NONLINEAR EQUATIONS
  16. M.A. Hafiz, Salwa M. H. Al-Goria: SOLVING NONLINEAR EQUATIONS USING A NEW TENTH-AND SEVENTH-ORDER METHODS FREE FROM SECOND DERIVATIVE
  17. Newton Basins
  18. Simon Tatham: Fractals derived from Newton-Raphson iteration
  19. Images des Maths: La méthode de Newton et son fractal
  20. Robert L. Devaney: Recent Research Papers
  21. John Whitehouse: Newton-Raphson Patterns
  22. Gregory Louis Zitelli: Fractals From Root Finding Algorithms
  23. efg's Computer Lab Fractals & Chaos: Glynn Function Study Center Gallery
  24. Daniel Ashlock: Real and complex fractals.
  25. Kai Schröder: Fraktale und Chemie --- Eine Einführung
  26. Adam Majewski: Fractals
  27. Mikael Hvidtfeldt Christensen: Distance Estimation
  28. Patrick Rammelt: 3D-Fraktale
  29. Christian Symmank: Bilder der Mandelbrot-Menge
  30. Xander Henderson: Newton Fractals
  31. Distance estimation for Newton fractals
  32. Dr. rer. nat. Lutz Lehmann: Julia-like fractals for roots finding methods
  33. Florian Brucker: Fractals from Iterated Root-Finding Methods
  34. Pictures of Julia and Mandelbrot sets
  35. Michael Becker: Some Julia sets
  36. Paul Bourke: Julia Set Fractal (2D)
  37. Evgeny Demidov: The Mandelbrot and Julia sets Anatomy Contents
  38. Ingvar Kullberg: The chaotic series of fractal articles
  39. Fraczine: Newton Raphson
  40. William Gilbert: Fractal Gallery
  41. Bart D. Stewart: Newton, Chebyshev, and Halley Basins of Attraction; A Complete Geometric Approach
  42. Yongil Kim: New Sixth-Order Improvements of the Jarratt Method
  43. Muhammad Rafiullah: A NEW SIXTH ORDER ITERATIVE METHOD FOR NONLINEAR EQUATIONS
  44. Changbum Chuna, Beny Neta: Some modification of Newton's method by the method of undetermined coefficients
  45. Farooq Ahmad, a Sajjad Hussain, Sifat Hussain, Arif Rafiq: New Efficient Fourth Order Method for Solving Nonlinear Equations
  46. M. Heydari, S. M. Hosseini, G. B. Loghmani: ON TWO NEW FAMILIES OF ITERATIVE METHODS FOR SOLVING NONLINEAR EQUATIONS WITH OPTIMAL ORDER
  47. J. Jayakumar: Generalized Simpson-Newton's Method for Solving Nonlinear Equations with Cubic Convergence
  48. Ramandeep Behl and S. S. Motsa: Geometric construction of eighth-order optimal families of Ostrowski's method
  49. Jishe Feng: A New Two-step Method for Solving Nonlinear Equations
  50. Tahereh Eftekhari:: A New Sixth-Order Steffensen-Type Iterative Method for Solving Nonlinear Equations
  51. Shengfeng Li, Rujing Wang: Two Fourth-order Iterative Methods Based on Continued Fraction for Root-finding Problems
  52. Sanjay K. Khattri and S. Abbasbandy: OPTIMAL FOURTH ORDER FAMILY OF ITERATIVE METHODS
  53. B. Neta: On Popovski's method for nonlinear equations
  54. Sanjay K Khattri and Ioannis K Argyros: Unification of sixth-order iterative methods
  55. M. Heydari and G.B. Loghmani: Third-Order and Fourth-Order Iterative Methods Free from Second Derivative for Finding Multiple Roots of Nonlinear Equations
  56. Sanjay Kumar Khattri: Quadrature Based Optimal Iterative Methods with Applications in High-Precision Computing
  57. Reza Ezzati1, Elham Azadegan: A simple iterative method with fifth-order convergence by using Potra and Ptak's method
  58. F. Mirzaee and A. Hamzeh: Sixth Order Method for Solving Nonlinear Equations
  59. JUAN L. VARONA: GRAPHIC AND NUMERICAL COMPARISON BETWEEN ITERATIVE ME
  60. Chi Chun-Mei and Feng Gao: A Few Numerical Methods for Solving Nonlinear Equations
  61. The Collatz Conjecture as a motivator for Complexity and Chaos
  62. Wikipedia: Collatz-Problem
  63. Hochschule für Angewandte Wissenschaften Hamburg: Das Collatz-Problem
  64. Muhammad Rafiullah und Muhammad Haleem: Three-Step Iterative Method with Sixth Order Convergence for Solving Nonlinear Equations
  65. Malik Zaka Ullah, Lala Muhammad Assas, Fayyaz Ahmad, A.S. Al-Fhaid: A correction note on "Three-Step Iterative Methods with Sixth Order Convergence for Solving Nonlinear Equations"
  66. R. Ezzati und F. Saleki: On the Construction of New Iterative Methods with Fourth-Order Convergence by Combining Previous Methods
  67. FAYYAZ AHMAD AND D. GARCA-SENZ: IMPROVING THREE-POINT ITERATIVE METHODS FOR SOLVING NONLINEAR EQUATIONS
  68. R. Thukral: Two-step Iterative Methods with Sixth-order Convergence for Solving Nonlinear Equations
  69. Sara T. M. Suleiman: Solving System of Nonlinear Equations Using Methods in the Halley Class
  70. Sanjay K. Khattri, Ioannis K. Argyros: HOW TO DEVELOP FOURTH AND SEVENTH ORDER ITERATIVE METHODS?
  71. M. Matin Far, M. Aminzadeh, S. Asadpour: A New Three-step Iterative Method for Solving Nonlinear Equations
  72. Alicia Cordero, Juan R. Torregrosa, Pura Vindel: Dynamics of a family of Chebyshev-Halley type methods
  73. Dissertation Arnd Lauber: On the Stability of Julia Sets of Functions having Baker Domains
  74. Dissertation Erin Elizabeth Williams: Categorization of all Newton maps of rational functions conjugate to quadratic polynomials
  75. Wolf Jung: Local and asymptotic similarity in one-parameter families
  76. K.Karthikeyan, S.K.Khadar Babu, M.Sundaramurthy, B.Rajesh Anand: SOME MULTI-STEP ITERATIVE ALGORITHMS FOR MINIMIZATION OF UNCONSTRAINED NON LINEAR FUNCTIONS
  77. Paul Bourke: Apollonian Gasket
  78. Wikipedia: Apollonian Gasket
  79. Wolfram Mathworld : Apollonian Gasket
  80. Wikipedia: Satz von Descartes
  81. Jasper Weinrich-Burd: A Thompson-Like Group for the Bubble Bath Julia Set
  82. Fractal Geometry: Differences between ‘Julia Set’ and ‘Julius Newtree Set’
  83. hpdz.net : The Nova Fractal
  84. The Online Fractal Generator : Newtonian Fractals
  85. Fractint: Summary of Fractal Types
  86. Sierpinski Curve Julia Sets of Rational Maps
  87. A Sierpinski Mandelbrot spiral for rational maps of the form Zm + lamda/Zn
  88. Cantor Necklaces and Structurally Unstable Sierpinski Curve Julia Sets for Rational Maps
  89. Checkerboard Julia Sets for Rational Maps
  90. On the Hausdorff Dimension of the Sierpinski Julia Sets
  91. ON THE HAUSDORFF DIMENSION OF JULIA SETS OF SOME REAL POLYNOMIALS
  92. AREA AND HAUSDORFF DIMENSION OF SIERPINSKI CARPET JULIA SETS
  93. On Hausdorff dimension of polynomial not totally disconnected Julia sets
  94. The Hausdorff Dimension of the Julia Set of Polynomials of the Form zd + c
  95. C. McMullen: Riemann surfaces, dynamics and geometry
  96. Conformal Dynamics and Hyperbolic Geometry
  97. Seminar Dynamics in One Complex Variable: Fatou und Julia Mengen
  98. Mapping Class Groups of Rational Maps
  99. Julia Sets in Parameter Spaces
  100. Julia Sets of Complex Polynomials and Their Implementation on the Computer
  101. Exploring the Mandelbrot set. The Orsay Notes.
  102. Die Nutzbarkeit von Fraktalen in VFX Produktionen
  103. SOME STRUCTURAL AND DYNAMICAL PROPERTIES OF MANDELBROT SET
  104. Inventive Burning Ship
  105. New-Fangled Mandelbrot and Julia Sets for Logarithmic Function
  106. Analysis of New-Fangled Mandelbrot Sets Controlled by TAN Function
  107. Algebraic Geometry of Discrete Dynamics - The case of one variable
  108. NEW APPROXIMATIONS FOR THE AREA OF THE MANDELBROT SET
  109. A Visual Analysis of Calculation-Paths of the Mandelbrot Set
  110. ALGORITHMS FOR COMPUTING ANGLES IN THE MANDELBROT SET
  111. AN EFFECTIVE ALGORITHM TO COMPUTE MANDELBROT SETS IN PARAMETER PLANES
  112. Chaotic bands in the Mandelbrot set
  113. HOW TO WORK WITH ONE-DIMENSIONAL QUADRATIC MAPS
  114. OPERATING WITH EXTERNAL ARGUMENTS IN THE MANDELBROT SET ANTENNA
  115. Misiurewicz point patterns generation in one-dimensional quadratic maps
  116. EXTERNAL ARGUMENTS FOR THE CHAOTIC BANDS CALCULATION IN THE MANDELBROT SET
  117. EQUIVALENCE BETWEEN SUBSHRUBS AND CHAOTIC BANDS IN THE MANDELBROT SET
  118. Julia sets appear quasiconformally in the Mandelbrot set
  119. Calculation of the Structure of a Shrub in the Mandelbrot Set
  120. Operating with External Arguments of Douady and Hubbard
  121. External arguments of Douady cauliflowers in the Mandelbrot set
  122. A Method to Solve the Limitations in Drawing External Rays of the Mandelbrot Set
  123. Renormalization and embedded Julia sets in the Mandelbrot set
  124. INTERNAL ADDRESSES OF THE MANDELBROT SET AND GALOIS GROUPS OF POLYNOMIALS
  125. Internal addresses in the Mandelbrot set and irreducibility of polynomials
  126. Self-similarity of the Mandelbrot set
  127. Similarity Between the Mandelbrot Set and Julia Sets
  128. Similarity of the Mandelbrot Set and Julia Sets - A Closer Look at Misiurewicz Points
  129. PACMAN RENORMALIZATION AND SELF-SIMILARITY OF THE MANDELBROT SET NEAR SIEGEL PARAMETERS
  130. Zalcman functions and similarity between the Mandelbrot set, Julia sets, and the tricorn
  131. Lecture 20 - Introduction to complex dynamics - 3/3: Mandelbrot and friends
  132. Lecture 19 - Introduction to complex dynamics - 2/3: Julia and Fatou
  133. Lecture 18 - Introduction to complex dynamics - 1/3
  134. Notes on Tan’s theorem on similarity between the Mandelbrot set and the Julia sets
  135. Dynamics of Chaotic Systems and Fractals
  136. DYNAMICS FOR CHAOS AND FRACTALS
  137. Dynamics, Chaos, and Fractals (part 5): Introduction to Complex Dynamics
  138. CHAPTER 1: Complex Dynamics: Chaos, Fractals, the Mandelbrot Set, and More
  139. CHAPTER 2: Soap films, Differential Geometry, and Minimal Surfaces
  140. CHAPTER 3: Applications to Flow Problems
  141. CHAPTER 4: Anamorphosis, Mapping Problems, and Harmonic Univalent Functions
  142. CHAPTER 5: Mappings to Polygonal Domains
  143. CHAPTER 6: Circle Packing
  144. Intro
  145. Appendices
  146. Explorations in Complex Variables with Accompanying Applets: Undergraduate Research
  147. Explorations in Complex Variables with Accompanying Applets: Undergraduate Research
  148. Complex Analysis Topics for Undergraduates and Beginning Researchers: an Exploration with Unsolved Problems
  149. Komplexe dynamische Systeme, Wettbewerb "Jugend Forscht" 2005
  150. External arguments in the multiple-spiral medallions of the Mandelbrot set
  151. Surgery on the Limbs of the Mandelbrot Set
  152. Extension of the Douady-Hubbard's Theorem on Convergence of Periodic External Rays of the Mandelbrot Set to Polynomials of type Ed
  153. Periodic Orbits, Externals Rays and the Mandelbrot Set: An Expository Account
  154. The Mandelbrot Set and the Farey Tree
  155. The Unexpected Fractal Signatures in Fibonacci Chains
  156. Bifurcation in Complex Quadratic Polynomial and Some Folk Theorems Involving the Geometry of Bulbs of the Mandelbrot Set
  157. The Mandelbrot Set and The Farey Tree, Robert L. Devaney
  158. Entropy, dimension and combinatorial moduli for one-dimensional dynamical systems, dissertation
  159. Checkerboard Julia Sets for Rational Maps
  160. RATIONAL MAPS: JULIA SETS FROM ACCESSIBLE MANDELBROT SETS ARE NOT HOMEOMORPHIC
  161. Rational maps with generalized Sierpinski gasket Julia sets
  162. Sierpi ´nski and non-Sierpi ´nski curve Julia sets in families of rational maps
  163. Spectral Analysis of Julia Sets, dissertation
  164. SINGULAR PERTURBATIONS OF zn
  165. Dynamics of rational maps
  166. Distance estimation method for drawing Mandelbrot and Julia sets
  167. Tricomplex Distance Estimation for Filled-in Julia Sets and Multibrot Sets
  168. Real-time rendering of complex fractals
  169. Hypercomplex Iterations, Distance Estimation and Higher Dimensional Fractals
  170. Efficiently generating the Mandelbrot and Julia sets, thesis
  171. EXPLICIT ESTIMATES ON DISTANCE ESTIMATOR METHOD FOR JULIA SETS OF POLYNOMIALS
  172. Generalized baby Mandelbrot sets adorned with halos in families of rational maps
  173. On the dynamics of generalized McMullen maps

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