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GAMM-Mitteilungen, 2006
AbstractThe Jacobi–Davidson method is a popular technique to compute a few eigenpairs of large sparse matrices. Its introduction, about a decade ago, was motivated by the fact that standard eigensolvers often require an expensive factorization of the matrix to compute interior eigenvalues.
Notay, Yvan, Hochstenbach, Michiel
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AbstractThe Jacobi–Davidson method is a popular technique to compute a few eigenpairs of large sparse matrices. Its introduction, about a decade ago, was motivated by the fact that standard eigensolvers often require an expensive factorization of the matrix to compute interior eigenvalues.
Notay, Yvan, Hochstenbach, Michiel
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2002
This survey paper gives the latest results on numerical accuracy and asymptotic convergence of various Jacobi-type methods.
Zlatko Drmač +2 more
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This survey paper gives the latest results on numerical accuracy and asymptotic convergence of various Jacobi-type methods.
Zlatko Drmač +2 more
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On the Condition Behaviour in the Jacobi Method
SIAM Journal on Matrix Analysis and Applications, 1996The aim of this note is to show that the matrix $S(n, \alpha)=(1-\alpha)I+\alpha ee^T$, $e=(1, \ldots, 1)^T$, $\alpha\in(0, 1)$ is not a counterexample for the accuracy properties of the Jacobi method for computing the singular and eigenvalue decomposition, as might be nderstood from a recent article of Mascarenhas in this journal.
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Rankin’s method and jacobi forms
Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg, 1997X ; 1 ; 1 ; 5 ; scie ...
Choie, Y, Kohnen, W
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An extension of the Hamilton-Jacobi method
Journal of Applied Mathematics and Mechanics, 1996Abstract A method of solving the canonical Hamilton equations, based on a search for invariant manifolds, which are uniquely projected onto position space, is proposed. These manifolds are specified by covector fields, which satisfy a system of first-order partial differential equations, similar in their properties to Lamb's equations in the dynamic ...
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Accelerating the CBFM-enhanced jacobi method
2017 International Conference on Electromagnetics in Advanced Applications (ICEAA), 2017The Characteristic Basis Function Method (CBFM)-enhanced Jacobi method has been introduced as an improvement to the standard iterative Jacobi method for finite array analysis. This technique is a domain decomposition approach based on the Method of Moments (MoM) formulation. In some cases, e.g.
Matthys M. Botha +3 more
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On the Convergence of Cyclic Jacobi Methods
IMA Journal of Applied Mathematics, 1975In a cyclic Jacobi method for calculating the eigenvalues and eigenvectors of a symmetric matrix, the pivots are chosen in any fixed cyclic order. It is not known in theory whether convergence to the solution is always obtained, although convergence has been proved subject to a restriction on the angle of rotation about each pivot (Henrici, 1958).
K. W. Brodlie, M. J. D. Powell
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Toda Chains in the Jacobi Method
Theoretical and Mathematical Physics, 2004We use the Jacobi method to construct various integrable systems, such as the Stackel systems and Toda chains, related to various root systems. We find canonical transformations that relate integrals of motion for the generalized open Toda chains of types Bn, Cn, and Dn.
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2013
In the preceding chapters, the predominant issues have been those connected with the deductive method: existence on the one hand, and the twin issues of regularity and necessary conditions on the other. We now introduce the reader to verification functions, a technique which unifies all the main inductive methods.
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In the preceding chapters, the predominant issues have been those connected with the deductive method: existence on the one hand, and the twin issues of regularity and necessary conditions on the other. We now introduce the reader to verification functions, a technique which unifies all the main inductive methods.
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