A Proof of Convergence for Two Parallel Jacobi SVD Algorithms
IEEE Transactions on Computers
On one-sided Jacobi methods for parallel computation
SIAM Journal on Algebraic and Discrete Methods
Efficient implementation of Jacobi algorithms and Jacobi sets on distributed memory architectures
Journal of Parallel and Distributed Computing - Special issue: algorithms for hypercube computers
Computation of the Euler angles of a symmetric 3X3 matrix
SIAM Journal on Matrix Analysis and Applications
Jacobi Sets for the Eigenproblem and Their Effect On Convergence Studied by Graphic Representations
Proceedings of the Fourth SIAM Conference on Parallel Processing for Scientific Computing
Jacobi-like Algorithms for Eigenvalue Decomposition of a Real Normal Matrix Using Real Arithmetic
IPPS '96 Proceedings of the 10th International Parallel Processing Symposium
Improving a parallel algorithm through a visual display
Journal of Computing Sciences in Colleges
An efficient method for computing eigenvalues of a real normal matrix
Journal of Parallel and Distributed Computing
| Hi-index | 0.00 |
We introduce a new method to reduce a real matrix to a real Schur form by a sequence of similarity transformations that are 3D orthogonal transformations. Two significant features of this method are that: all the transformed matrices and all the computations are done in the real field; and it can be easily parallelized. We call the algorithm that uses this method the real two-zero (RTZ) algorithm. We describe both serial and parallel implementations of the RTZ algorithm. Our tests indicate that the rate of convergence to a real Schur form is quadratic for real near-normal matrices with real distinct eigenvalues. Suppose n is the order of a real matrix A. In order to choose a sequence of 3D orthogonal transformations on A, we need to determine some ordering on triples in T={(k,l,m)|1⩽k