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implicitly restarted arnoldi method  (MathWorks Inc)


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    MathWorks Inc implicitly restarted arnoldi method
    Implicitly Restarted Arnoldi Method, supplied by MathWorks Inc, 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/10__1002_slash_nla__2418-222-31-42
    Average 90 stars, based on 1 article reviews
    implicitly restarted arnoldi method - by Bioz Stars, 2026-09
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    Article Title: Estimating and increasing the structural robustness of a network
    Article Snippet: In the rare occasions when this is not the case, we can compute an improved approximation by applying the (standard) Arnoldi method described, for example, by Saad,19 or the implicitly restarted (standard) Arnoldi method described in Reference 20 and implemented by the MATLAB function eigs.

    Article Title: Second-order adjoint-based sensitivity for hydrodynamic stability and control
    Article Snippet: Stability analysis The eigenvalue problem (2.5) is solved with Matlab using an implicitly restarted Arnoldi method with shift-and-invert preconditioning.

    Article Title: Ice sheet flow with thermally activated sliding. Part 2: the stability of subtemperate regions
    Article Snippet: We deal with the singularity of the mass matrix J M by means of row-reduction, and we then solve the row-reduced eigenvalue problem with an implicitly restarted Arnoldi method as implemented in ARPACK for Matlab [ 19 ].



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    implicitly restarted arnoldi method matlab/arpack  (MathWorks Inc)
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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