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Systolic array implementation of the Jacobi decomposition  

Systolic array implementation of the Jacobi decomposition  

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Although we find it an efficient method to observe characteristics of the signal surface, on-line eigenanalysis is still not commonly in use in digital signal processing applications. By performing eigendecomposition on a signal correlation matrix, several DSP problems such as spectral estimation and adaptive filtering can be solved.

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... Equations 10 and 11 are the key to the parallelism inherent in Jacobi's algorithm. The time parallel aspects have been well explored [2] [6], although in this study we show that there are still some improvements to be made in the details. What has not been fully explored is the utility of the space parallelism of Jacobi's method. ...
... Equations 10 and 11 are the key to the parallelism inherent in Jacobi's algorithm. The time parallel aspects have been well explored [2, 6], although in this study we show that there are still some improvements to be made in the details. What has not been fully explored is the utility of the space parallelism of Jacobi's method. ...
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Matrix diagonalization is an important component of many aspects of computational science. There are a vari- ety of algorithms to accomplish this task. Jacobi's algo- rithm is a good choice for parallel environments. Jacobi's algorithm consists of a series of matrix plane rotations, the ordering of which can dramatically affect performance. We show a new ordering which cuts the number of necessary operations approximately in half. Additionally, Jacobi's algorithm can be made parallel in space as well as time. This is an advantage when deal- ing with very large matrices, such as those found in quan- tum chemistry.
... For all Jacobi variants, the convergence is asymptotically quadratic. Our decision to use Jacobi methods is their inherent parallelism, and because very similar solutions can be used for both of the procedures proposed in [10]. ...
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... It has been shown [17] that the cyclic by rows ordering and condition (3.3) ensure convergence of the Jacobi method applied to A T A and convergence of the cyclic by rows Hestenes method follows. ...
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