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implicitly restarted arnoldi method matlab/arpack  (MathWorks Inc)
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MathWorks Inc implicitly restarted arnoldi method matlab/arpack
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.
Implicitly Restarted Arnoldi Method Matlab/Arpack, 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
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implicitly restarted arnoldi method  (MathWorks Inc)
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MathWorks Inc implicitly restarted arnoldi method
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.
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
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implicitly restarted arnoldi iteration method  (MathWorks Inc)
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MathWorks Inc implicitly restarted arnoldi iteration method
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.
Implicitly Restarted Arnoldi Iteration 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
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irlm  (MathWorks Inc)
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MathWorks Inc irlm
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.
Irlm, 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
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implicitly restarted arnoldi  (MathWorks Inc)
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MathWorks Inc implicitly restarted arnoldi
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.
Implicitly Restarted Arnoldi, 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
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function eigs  (MathWorks Inc)
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MathWorks Inc function eigs
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.
Function Eigs, 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
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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