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  2. Power iteration - Wikipedia

    en.wikipedia.org/wiki/Power_iteration

    #!/usr/bin/env python3 import numpy as np def power_iteration (A, num_iterations: int): # Ideally choose a random vector # To decrease the chance that our vector # Is orthogonal to the eigenvector b_k = np. random. rand (A. shape [1]) for _ in range (num_iterations): # calculate the matrix-by-vector product Ab b_k1 = np. dot (A, b_k) # calculate the norm b_k1_norm = np. linalg. norm (b_k1 ...

  3. Arnoldi iteration - Wikipedia

    en.wikipedia.org/wiki/Arnoldi_iteration

    In numerical linear algebra, the Arnoldi iteration is an eigenvalue algorithm and an important example of an iterative method.Arnoldi finds an approximation to the eigenvalues and eigenvectors of general (possibly non-Hermitian) matrices by constructing an orthonormal basis of the Krylov subspace, which makes it particularly useful when dealing with large sparse matrices.

  4. NumPy - Wikipedia

    en.wikipedia.org/wiki/NumPy

    NumPy (pronounced / ˈ n ʌ m p aɪ / NUM-py) is a library for the Python programming language, adding support for large, multi-dimensional arrays and matrices, along with a large collection of high-level mathematical functions to operate on these arrays. [3]

  5. Moore–Penrose inverse - Wikipedia

    en.wikipedia.org/wiki/Moore–Penrose_inverse

    The Python package NumPy provides a pseudoinverse calculation through its functions matrix.I and linalg.pinv; its pinv uses the SVD-based algorithm. SciPy adds a function scipy.linalg.pinv that uses a least-squares solver. The MASS package for R provides a calculation of the Moore–Penrose inverse through the ginv function. [24]

  6. Successive over-relaxation - Wikipedia

    en.wikipedia.org/wiki/Successive_over-relaxation

    import numpy as np from scipy import linalg def sor_solver (A, b, omega, initial_guess, convergence_criteria): """ This is an implementation of the pseudo-code provided in the Wikipedia article.

  7. Cholesky decomposition - Wikipedia

    en.wikipedia.org/wiki/Cholesky_decomposition

    In Python, the function cholesky from the numpy.linalg module performs Cholesky decomposition. In Matlab, the chol function gives the Cholesky decomposition. Note that chol uses the upper triangular factor of the input matrix by default, i.e. it computes = where is upper triangular. A flag can be passed to use the lower triangular factor instead.

  8. Matrix norm - Wikipedia

    en.wikipedia.org/wiki/Matrix_norm

    Suppose a vector norm ‖ ‖ on and a vector norm ‖ ‖ on are given. Any matrix A induces a linear operator from to with respect to the standard basis, and one defines the corresponding induced norm or operator norm or subordinate norm on the space of all matrices as follows: ‖ ‖, = {‖ ‖: ‖ ‖ =} = {‖ ‖ ‖ ‖:}. where denotes the supremum.

  9. Comparison of linear algebra libraries - Wikipedia

    en.wikipedia.org/wiki/Comparison_of_linear...

    Matrix types (special types like bidiagonal/tridiagonal are not listed): Real – general (nonsymmetric) real; Complex – general (nonsymmetric) complex; SPD – symmetric positive definite (real)