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feat(numerical_methods): Add Neville's Algorithm #3045

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@Keykyrios Keykyrios commented Oct 20, 2025

Description of Change

This PR adds a C++ implementation of Neville's Algorithm for polynomial interpolation. The algorithm is placed in the numerical_methods directory.

The implementation includes:

  • A function interpolate() within a dedicated namespace.
  • Doxygen-style comments explaining the file, function, and parameters.
  • A test() function with assertions to verify correctness for linear, quadratic, and negative-valued cases.

Wikipedia: https://en.wikipedia.org/wiki/Neville%27s_algorithm

Checklist

  • Added description of change
  • Added file name matches File name guidelines (nevilles_algorithm.cpp)
  • Added tests and example, test must pass
  • Added documentation so that the program is self-explanatory and educational - Doxygen guidelines
  • Relevant documentation/comments is changed or added
  • PR title follows semantic commit guidelines
  • Search previous suggestions before making a new one, as yours may be a duplicate.
  • I acknowledge that all my contributions will be made under the project's license.

Notes: Adds an implementation of Neville's algorithm for polynomial interpolation.

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@Panquesito7 Panquesito7 Awaiting requested review from Panquesito7 Panquesito7 is a code owner

@realstealthninja realstealthninja Awaiting requested review from realstealthninja realstealthninja is a code owner

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