Weierstrass Method #12877
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Weierstrass Method #12877
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- Implements Durand-Kerner (Weierstrass) method for polynomial root finding - Accepts user-defined polynomial function and degree - Uses random perturbation of complex roots of unity for initial guesses - Handles validation, overflow clipping, and includes doctest
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Describe your change:
This pull request adds an implementation of the Weierstrass (Durand–Kerner) method to numerically approximate all complex roots of a given polynomial. The function accepts a user-defined polynomial, its degree, and an optional initial guess for the roots. The implementation includes:
Type annotations and detailed docstring
Doctest to validate correctness
Optional support for custom initial guesses
Numerical safeguards (e.g., overflow clipping)
A Wikipedia reference for further explanation
This method is useful in numerical analysis and computational algebra for finding all roots of a polynomial simultaneously using iterative refinement.
Checklist: