By Topic

The real two-zero algorithm: a parallel algorithm to reduce a real matrix to a real Schur form

Sign In

Cookies must be enabled to login.After enabling cookies , please use refresh or reload or ctrl+f5 on the browser for the login options.

Formats Non-Member Member
$31 $13
Learn how you can qualify for the best price for this item!
Become an IEEE Member or Subscribe to
IEEE Xplore for exclusive pricing!
close button

puzzle piece

IEEE membership options for an individual and IEEE Xplore subscriptions for an organization offer the most affordable access to essential journal articles, conference papers, standards, eBooks, and eLearning courses.

Learn more about:

IEEE membership

IEEE Xplore subscriptions

2 Author(s)
Mantharam, M. ; Dept. of Math., City Univ. of New York, NY, USA ; Eberlein, P.J.

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<l<m⩽n}, where (k,l,m) defines the three coordinates under the 3D transformation. We show how the ordering of the triples used in our implementations can be generated cyclically in an algorithm

Published in:

Parallel and Distributed Systems, IEEE Transactions on  (Volume:6 ,  Issue: 1 )