Fractals from Polynomial Solutions 1.0 Download

Fractals from Polynomial Solutions 1.0 Description

"Solving a linear algebraic equation,find the roots of a second-order polynomial"

Editor: Solving a linear algebraic Equation is a simple process and to find the roots of a second-order polynomial, we use the quadratic equation. There are also specific procedures for finding the roots of a third-order polynomial. However, for fourth-order and higher, we need other ways to find roots. In this paper (Fractals FROM POLYNOMIAL SOLUTIONS), we study the Newton-Raphson method for finding roots. To use the Newton-Raphson method to find polynomial roots, we need an initial guess at a root. Every point in the complex plane is a potential solution, hence a potential guess. If we use each point in the complex plane as an initial guess, compute the resulting converged root, and track which guess converged to which root, we obtain a mapping of initial guesses to final roots. This mapping, when drawn in color on a computer screen, can provide pretty and surprising results. Such mappings are fractals. We develop a procedure for generating fractals from the solution of a general polynomial. For each step in the procedure, the pertinent equations are provided to help you understand the technique and develop your own computer routine (with modifications, if desired). you can free download Fractals from Polynomial Solutions 1.0 now.

Fractals from Polynomial Solutions 1.0 Keywords

mia, solutions, fractals, fractal

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