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
[x ] 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.
[x] This pull request is all my own work -- I have not plagiarized.
[x] I know that pull requests will not be merged if they fail the automated tests.
[x] 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.
[x] All functions and variable names follow Python naming conventions.
[x] All function parameters and return values are annotated with Python type hints.
[ ] All functions have doctests that pass the automated testing.
[x] 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".
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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