Quasi-Polynomial Mapping-based Root-Finder
时间: 2024-01-18 11:02:39 浏览: 31
Quasi-polynomial mapping-based root-finder is a numerical method used to find the roots of a given polynomial equation. It is an iterative method that uses a quasi-polynomial mapping function to transform the polynomial equation into a linear equation. The method works by iteratively solving the linear equation until the root of the original polynomial equation is found.
The quasi-polynomial mapping function is a polynomial function of two variables that maps the complex plane to itself. The function is defined as follows:
f(z) = z^d + a_1(z)z^(d-1) + a_2(z)z^(d-2) + ... + a_d-1(z)z + a_d(z)
where d is the degree of the polynomial equation, a_i(z) are polynomial functions of z of degree at most d-i, and z is a complex variable.
To use the quasi-polynomial mapping-based root-finder, the following steps are performed:
1. Choose an initial guess for the root of the polynomial equation.
2. Apply the quasi-polynomial mapping function to the initial guess.
3. Solve the resulting linear equation for the new value of the guess.
4. Repeat steps 2 and 3 until the difference between successive guesses is less than a specified tolerance.
The quasi-polynomial mapping-based root-finder has the advantage of being able to find multiple roots of a polynomial equation, including roots with multiplicity greater than one. It is also relatively fast and efficient compared to other root-finding methods. However, it may not always converge to the correct root, particularly for polynomial equations with multiple roots that are close together.
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