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Weierstrass Method #12877

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@aditya7balotra aditya7balotra commented Aug 2, 2025 •
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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

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:

  1. Type annotations and detailed docstring

  2. Doctest to validate correctness

  3. Optional support for custom initial guesses

  4. Numerical safeguards (e.g., overflow clipping)

  5. 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.

  • Add an algorithm?
  • Fix a bug or typo in an existing algorithm?
  • Add or change doctests? -- Note: Please avoid changing both code and tests in a single pull request.
  • Documentation change?

Checklist:

  • I have read CONTRIBUTING.md.
  • This pull request is all my own work -- I have not plagiarized.
  • I know that pull requests will not be merged if they fail the automated tests.
  • This PR only changes one algorithm file. To ease review, please open separate PRs for separate algorithms.
  • All new Python files are placed inside an existing directory.
  • All filenames are in all lowercase characters with no spaces or dashes.
  • All functions and variable names follow Python naming conventions.
  • All function parameters and return values are annotated with Python type hints.
  • All functions have doctests that pass the automated testing.
  • All new algorithms include at least one URL that points to Wikipedia or another similar explanation.
  • If this pull request resolves one or more open issues then the description above includes the issue number(s) with a closing keyword: "Fixes #ISSUE-NUMBER".

@aditya7balotra
Add weierstrass_method for approximating complex roots
3c720e5 
- 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
@algorithms-keeper algorithms-keeper bot added the awaiting reviews This PR is ready to be reviewed label Aug 2, 2025
@helma436
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helma436 commented Aug 4, 2025

Preparing review...

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@helma436
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helma436 commented Aug 4, 2025

Preparing review...

@helma436
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helma436 commented Aug 4, 2025

Preparing review...

@helma436
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helma436 commented Aug 4, 2025

Preparing review...

@MrittikaDutta
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Currently, the method always runs max_iter iterations. Adding a tolerance (tol) and stopping early when updates are small would improve efficiency.

@MrittikaDutta
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For stability, sometimes using deflation or derivative checks helps avoid stagnation on multiple roots. Could be an optional enhancement.

@MrittikaDutta
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Constructing the full denominator matrix (degree x degree) is O(n²).
You might optimize by computing products without building a dense matrix.

@aditya7balotra
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Great feedback, @MrittikaDutta !
Your suggestions are really valuable, and I’ll consider implementing them soon.
Thanks a lot!

CaedenPH
CaedenPH requested changes Aug 28, 2025
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Looks good 👍
Requires some additional tests ideally with higher order, handling floats, does this algorithm handle complex roots, etc
If you add some more tests or commit my tests I'll merge this pr.

@CaedenPH CaedenPH added awaiting changes A maintainer has requested changes to this PR and removed awaiting reviews This PR is ready to be reviewed labels Aug 28, 2025
@algorithms-keeper algorithms-keeper bot added awaiting reviews This PR is ready to be reviewed tests are failing Do not merge until tests pass and removed awaiting changes A maintainer has requested changes to this PR labels Aug 28, 2025
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4 participants
@aditya7balotra @helma436 @MrittikaDutta @CaedenPH