Research and Advances

Data-flow algorithms for parallel matrix computation

In this article we develop some algorithms and tools for solving matrix problems on parallel processing computers. Operations are synchronized through data-flow alone, which makes global synchronization unnecessary and enables the algorithms to be implemented on machines with very simple operating systems and communication protocols. As examples, we present algorithms that form the main modules for solving Liapounov matrix equations. We compare this approach to wave front array processors and systolic arrays, and note its advantages in handling missized problems, in evaluating variations of algorithms or architectures, in moving algorithms from system to system, and in debugging parallel algorithms on sequential machines.


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Research and Advances

Incorporating origin shifts into the QR algorithm for symmetric tridiagonal matrices

The QR iteration for the eigenvalues of a symmetric tridiagonal matrix can be accelerated by incorporating a sequence of origin shifts. The origin shift may be either subtracted directly from the diagonal elements of the matrix or incorporated by means of an implicit algorithm. Both methods have drawbacks: the direct method can unnecessarily degrade small eigenvalues, while the implicit method can effectively loose the shift and thereby retard the convergence. This paper presents a new method which has neither drawback.

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