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Polynomial root-finding and polynomiography /
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 wi...
| Clasificación: | Libro Electrónico |
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| Autor principal: | |
| Formato: | Electrónico eBook |
| Idioma: | Inglés |
| Publicado: |
Singapore ; Hackensack, NJ :
World Scientific,
©2009.
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| Temas: | |
| Acceso en línea: | Texto completo |
Tabla de Contenidos:
- Approximation of square-roots and their visualizations
- The fundamental theorem of algebra and a special case of Taylor's theorem
- Introduction to the basic family and polynomiography
- Equivalent formulations of the basic family
- Basic family as dynamical system
- Fixed points of the basic family
- Algebraic derivation of the basic family and characterizations
- The truncated basic family and the case of Halley family
- Characterizations of solutions of homogeneous linear recurrence relations
- Generalization of Taylor's theorem and Newton's method
- The multipoint basic family and its order of convergence
- A computational study of the multipoint basic family
- A general determinantal lower bound
- Formulas for approximation of pi based on root-finding algorithms
- Bounds on roots of polynomials and analytic functions
- A geometric optimization and its algebraic offsprings
- Polynomiography : algorithms for visualization of polynomial equations
- Visualization of homogeneous linear recurrence relations
- Applications of polynomiography in art, education, science, and mathematics
- Approximation of square-roots revisited
- Further applications and extensions of the basic family and polynomiography.