Added the implementation of Lanczos algorithm #12386
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Changed argument name A to a Changed variable name V to v Added specifications for beta and alpha Changed np.random.randn
…e_pablo # Conflicts: # linear_algebra/lanczos_algorithm.py
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| def lanczos(a: np.ndarray) -> tuple[list[float], list[float]]: |
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As there is no test file in this pull request nor any test function or class in the file linear_algebra/lanczos_algorithm.py, please provide doctest for the function lanczos
Please provide descriptive name for the parameter: a
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Added an algorithm that calculates the coefficients of the Legendre polynomial of degree n using the recurrence relation.
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| import numpy as np | ||
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| def lanczos(a: np.ndarray) -> tuple[list[float], list[float]]: |
There was a problem hiding this comment.
As there is no test file in this pull request nor any test function or class in the file linear_algebra/lanczos_algorithm.py, please provide doctest for the function lanczos
Please provide descriptive name for the parameter: a
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Describe your change:
Added the implemenation of Lanczos algorithm.
The Lanczos algorithm is an iterative method used to compute the eigenvalues and eigenvectors of large, sparse symmetric matrices. It transforms the matrix into a smaller tridiagonal matrix that approximates the original matrix's spectral properties. The algorithm generates an orthogonal basis for the Krylov subspace, which is built from successive matrix-vector multiplications.
https://en.wikipedia.org/wiki/Lanczos_algorithm
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