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Reference implementations of Householder QR decomposition, Hessenberg reduction, eigenvalue QR-algorithm and QR-LLS using Eigen3 lib

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DmitriBogdanov/Householder-QR

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Project name

This project is a part of a numerical analysis course. It implements following algorithms:

  • QR-factorization using Householder reflections
  • Modification of QR-factorization for Linear Least Squares (LLS) problem
  • LLS solver using QR-decomposition method
  • Backwards Gaussian Elimination
  • Hessenberg reduction using Householder reflections
  • Modification of QR-factorization for upper-hessenberg matrices
  • Regular QR-algorithm
  • Shifted QR-algorithm with Hessenberg decomposition

Documentation

See report/report.pdf for implementation notes (ru). Most functions include proper in-code documentation (en).

Requirements

  • Requires C++17 support

Dependencies

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License

This project is licensed under the MIT License - see the LICENSE.md for details

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Reference implementations of Householder QR decomposition, Hessenberg reduction, eigenvalue QR-algorithm and QR-LLS using Eigen3 lib

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