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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).
Brodlie, K. W., Powell, M. J. D.
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Parallel Block-Jacobi SVD Methods
2012The serial Jacobi algorithm (either one-sided or two-sided) for the computation of a singular value decomposition (SVD) of a general matrix has excellent numerical properties and parallelization potential, but it is considered to be the slowest method for computing the SVD.
Martin Bečka +2 more
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Accelerating Block-Jacobi Methods
2003Until recently QR methods and their variations have been considered as the fastest methods for computing the singular value and the symmetric eigenvalue problems. Lately, Divide and Conquer methods have developed to a stage at which for larger matrices they overcome the performance of the QR methods. However, the both types of methods, require reducing
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The Hamilton-Jacobi method and Hamiltonian maps
Journal of Physics A: Mathematical and General, 2002Summary: A method for constructing time-step-based symplectic maps for a generic Hamiltonian system subjected to perturbation is developed. Using the Hamilton-Jacobi method and Jacobi's theorem in finite periodic time intervals, a general form of the symplectic maps is established. A generating function of the map is found by the perturbation method in
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The Jacobi method for real symmetric matrices
Numerische Mathematik, 1966As is well known, a real symmetric matrix can be transformed iteratively into diagonal form through a sequence of appropriately chosen elementary orthogonal transformations (in the following called Jacobi rotations): $${A_k} \to {A_{k + 1}} = U_k^T{A_k}{U_k}{\text{ (}}{A_0}{\text{ = given matrix),}}$$ where U k = U k(p,q, φ) is an orthogonal ...
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Improving Block-Jacobi Methods
1904A way how to exploit memory hierarchy to improve performance of some block methods, is explained for the case of a one-sided block-Jacobi method for computing SVD of rectangular matrices. At each step of that method, an orthogonal matrix U must be applied to two block-columns of the iterated matrix, $ [G_i, G_j]U$.
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Generalized eigensolutions by Jacobi methods
Zeitschrift für angewandte Mathematik und Mechanik, 1996Generalized eigenvalue problem ; Jacobi ...
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