On the Schur Decomposition of a Matrix for Parallel Computation
IEEE Transactions on Computers
The algebraic eigenvalue problem
The algebraic eigenvalue problem
SIAM Journal on Scientific and Statistical Computing
A one-sided Jacobi algorithm for computing the singular value decomposition on avector computer
SIAM Journal on Scientific and Statistical Computing
Efficient implementation of Jacobi algorithms and Jacobi sets on distributed memory architectures
Journal of Parallel and Distributed Computing - Special issue: algorithms for hypercube computers
Computing the Singular Value Decomposition on the Connection Machine
IEEE Transactions on Computers
Jacobi's method is more accurage than QR
SIAM Journal on Matrix Analysis and Applications
Hamilton and Jacobi Meet Again: Quaternions and the Eigenvalue Problem
SIAM Journal on Matrix Analysis and Applications
The Real Two-Zero Algorithm: A Parallel Algorithm to Reduce a Real Matrix to a Real Schur Form
IEEE Transactions on Parallel and Distributed Systems
On the Convergence of the Jacobi Method for Arbitrary Orderings
SIAM Journal on Matrix Analysis and Applications
Matrix computations (3rd ed.)
A parallel ring ordering algorithm for efficient one-sided Jacobi SVD computations
Journal of Parallel and Distributed Computing
Computing the Singular-Value Decomposition on the ILLIAC IV
ACM Transactions on Mathematical Software (TOMS)
Jacobi-like Algorithms for Eigenvalue Decomposition of a Real Normal Matrix Using Real Arithmetic
IPPS '96 Proceedings of the 10th International Parallel Processing Symposium
On parallel implementation of the one-sided Jacobi algorithm for singular value decompositions
PDP '95 Proceedings of the 3rd Euromicro Workshop on Parallel and Distributed Processing
Accelerating the SVD Block-Jacobi Method
Computing - Editorial: Special issue on GAMM – Workshop on Guaranteed Error-bounds for the Solution of Nonlinear Problems in Applied Mathematics
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Jacobi-based algorithms have attracted attention as they have a high degree of potential parallelism and may be more accurate than QR-based algorithms. In this paper we discuss how to design efficient Jacobi-like algorithms for eigenvalue decomposition on real normal matrix. We introduce a block Jacobi-like method. This method uses only real arithmetic and orthogonal similar transformations and achieves ultimate quadratic convergence. A theoretical analysis is conducted and some experimental results are presented.