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arnoldi algorithm  (Schmid GmbH)

 
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    Schmid GmbH arnoldi algorithm
    Arnoldi Algorithm, supplied by Schmid GmbH, used in various techniques. Bioz Stars score: 90/100, based on 1 PubMed citations. ZERO BIAS - scores, article reviews, protocol conditions and more
    https://www.bioz.com/product/implicitly+restarted+arnoldi+method/arnoldi+algorithm/pm23278096-498-4-27
    Average 90 stars, based on 1 article reviews
    arnoldi algorithm - by Bioz Stars, 2026-11
    90/100 stars

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    other:

    Article Title: Proper orthogonal decomposition and dynamic mode decomposition of jet in channel crossflow
    Article Snippet: However, they can be approximately calculated with the use of the Arnoldi algorithm as proposed by Schmid (2010).

    Variant Assay:

    Article Title: Applied Koopmanism.
    Article Snippet: .. A variant of the Arnoldi algorithm, utilizing companion matrices, was first described in Ruhe.44 The algorithm was popularized in the Fluids community by Rowley et al.43 and Schmid.47 In Schmid,47 the algorithm was dubbed the DMD, whereas Rowley et al.43 related the algorithm to the approximation of Koopman modes. ..



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    Comparison of convergence of the present inflation method with the Lanczos and Power methods. The computational time m (to calculate both the lowest eigenvalue and corresponding eigenvector) is the number of matrix-vector multiplications. Note that the original Lanczos method requires two matrix-vector multiplications per step if the eigenstate as well as the eigenvalue are to obtained at the end of the calculation without storing all intermediate vectors. The implicitly restarted <t>Arnoldi</t> method (MATLAB/ARPACK) behaves very similarly to Lanczos, and is not shown here (but see Fig. 1). (A and B) Results for some test matrices taken from ref. 11. (C) Results for a random sparse matrix. The matrix used in D corresponds to a model of strongly correlated spin-polarized fermions on a triangular lattice.
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    Comparison of convergence of the present inflation method with the Lanczos and Power methods. The computational time m (to calculate both the lowest eigenvalue and corresponding eigenvector) is the number of matrix-vector multiplications. Note that the original Lanczos method requires two matrix-vector multiplications per step if the eigenstate as well as the eigenvalue are to obtained at the end of the calculation without storing all intermediate vectors. The implicitly restarted Arnoldi method (MATLAB/ARPACK) behaves very similarly to Lanczos, and is not shown here (but see Fig. 1). (A and B) Results for some test matrices taken from ref. 11. (C) Results for a random sparse matrix. The matrix used in D corresponds to a model of strongly correlated spin-polarized fermions on a triangular lattice.

    Journal: Proceedings of the National Academy of Sciences of the United States of America

    Article Title: Inflationary dynamics for matrix eigenvalue problems

    doi: 10.1073/pnas.0801047105

    Figure Lengend Snippet: Comparison of convergence of the present inflation method with the Lanczos and Power methods. The computational time m (to calculate both the lowest eigenvalue and corresponding eigenvector) is the number of matrix-vector multiplications. Note that the original Lanczos method requires two matrix-vector multiplications per step if the eigenstate as well as the eigenvalue are to obtained at the end of the calculation without storing all intermediate vectors. The implicitly restarted Arnoldi method (MATLAB/ARPACK) behaves very similarly to Lanczos, and is not shown here (but see Fig. 1). (A and B) Results for some test matrices taken from ref. 11. (C) Results for a random sparse matrix. The matrix used in D corresponds to a model of strongly correlated spin-polarized fermions on a triangular lattice.

    Article Snippet: The implicitly restarted Arnoldi method (MATLAB/ARPACK) behaves very similarly to Lanczos, and is not shown here (but see ). ( A and B ) Results for some test matrices taken from ref. 11 . ( C ) Results for a random sparse matrix.

    Techniques: Comparison, Plasmid Preparation

    The convergence of the inflation method for the lowest four eigenpairs of a test matrix (11) is compared with the implicitly restarted Arnoldi method (as implemented in MATLAB/ARPACK). Exact eigenvalues are indicated by horizontal lines. In the inflation method, we diagonalize in a six-dimensional basis after every 6 dynamical steps. In the Arnoldi calculation, we use a basis of size 12. In each case, the computational time m represents the number of matrix-vector multiplications (i.e., we do not multiply Arnoldi iterations by 2, and we do count every matrix-vector multiplication on the horizontal axis; e.g., when inflating 6 eigenvalues, we count 6 matrix-vector multiplcations per iteration step).

    Journal: Proceedings of the National Academy of Sciences of the United States of America

    Article Title: Inflationary dynamics for matrix eigenvalue problems

    doi: 10.1073/pnas.0801047105

    Figure Lengend Snippet: The convergence of the inflation method for the lowest four eigenpairs of a test matrix (11) is compared with the implicitly restarted Arnoldi method (as implemented in MATLAB/ARPACK). Exact eigenvalues are indicated by horizontal lines. In the inflation method, we diagonalize in a six-dimensional basis after every 6 dynamical steps. In the Arnoldi calculation, we use a basis of size 12. In each case, the computational time m represents the number of matrix-vector multiplications (i.e., we do not multiply Arnoldi iterations by 2, and we do count every matrix-vector multiplication on the horizontal axis; e.g., when inflating 6 eigenvalues, we count 6 matrix-vector multiplcations per iteration step).

    Article Snippet: The implicitly restarted Arnoldi method (MATLAB/ARPACK) behaves very similarly to Lanczos, and is not shown here (but see ). ( A and B ) Results for some test matrices taken from ref. 11 . ( C ) Results for a random sparse matrix.

    Techniques: Plasmid Preparation