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  2. Jacobi eigenvalue algorithm - Wikipedia

    en.wikipedia.org/wiki/Jacobi_eigenvalue_algorithm

    The Jacobi Method has been generalized to complex Hermitian matrices, general nonsymmetric real and complex matrices as well as block matrices. Since singular values of a real matrix are the square roots of the eigenvalues of the symmetric matrix = it can also be used

  3. Jacobi method for complex Hermitian matrices - Wikipedia

    en.wikipedia.org/wiki/Jacobi_Method_for_Complex...

    The complex unitary rotation matrices R pq can be used for Jacobi iteration of complex Hermitian matrices in order to find a numerical estimation of their eigenvectors and eigenvalues simultaneously. Similar to the Givens rotation matrices , R pq are defined as:

  4. Eigenvalue algorithm - Wikipedia

    en.wikipedia.org/wiki/Eigenvalue_algorithm

    Given an n × n square matrix A of real or complex numbers, an eigenvalue λ and its associated generalized eigenvector v are a pair obeying the relation [1] =,where v is a nonzero n × 1 column vector, I is the n × n identity matrix, k is a positive integer, and both λ and v are allowed to be complex even when A is real.l When k = 1, the vector is called simply an eigenvector, and the pair ...

  5. SLEPc - Wikipedia

    en.wikipedia.org/wiki/SLEPc

    Davidson methods such as Generalized Davidson and Jacobi-Davidson. Conjugate gradient methods such as LOBPCG. A contour integral solver (CISS). Interface to some external eigensolvers, such as ARPACK and BLOPEX. Customization options include: number of wanted eigenvalues, tolerance, size of the employed subspaces, part of the spectrum of interest.

  6. Jacobi method - Wikipedia

    en.wikipedia.org/wiki/Jacobi_method

    In numerical linear algebra, the Jacobi method (a.k.a. the Jacobi iteration method) is an iterative algorithm for determining the solutions of a strictly diagonally dominant system of linear equations. Each diagonal element is solved for, and an approximate value is plugged in. The process is then iterated until it converges.

  7. Matrix-free methods - Wikipedia

    en.wikipedia.org/wiki/Matrix-free_methods

    It is generally used in solving non-linear equations like Euler's equations in computational fluid dynamics. Matrix-free conjugate gradient method has been applied in the non-linear elasto-plastic finite element solver. [7] Solving these equations requires the calculation of the Jacobian which is costly in terms of CPU time and storage. To ...

  8. Category:Numerical linear algebra - Wikipedia

    en.wikipedia.org/wiki/Category:Numerical_linear...

    Numerical linear algebra is the intersection of numerical analysis and linear algebra: its purpose is the design and analysis of algorithms for the numerical solution of matrix problems. The most important problems are the solution of a system of linear equations and the determination of eigenvalues .

  9. List of finite element software packages - Wikipedia

    en.wikipedia.org/wiki/List_of_finite_element...

    Free: Linux, Windows: CalculiX: It is an Open Source FEA project. The solver uses a partially compatible ABAQUS file format. The pre/post-processor generates input data for many FEA and CFD applications: Guido Dhondt, Klaus Wittig: 2.20: 2022-08-01: GNU GPL: Free: Linux, Windows: DIANA FEA