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The Computer Journal 1990 33(3):252-260; doi:10.1093/comjnl/33.3.252
© 1990 by British Computer Society
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On the Design of an Integrated Systolic Array for Solving Simultaneous Linear Equations

F.-C. Lin * and K. Chen

Department of Computer Science and Information Engineering, National Taiwan University, Taipei, Taiwan, China

This paper introduces, in a stepwise refinement manner, a new systolic array for solving simultaneous linear equations AX = B, where A is an n x n matrix and B is an n x m matrix. Instead of using conventional matrix triangularisation, our design is based on a generalised Gauss–Jordan elimination procedure. First A is transformed into a permutation matrix P and B is transformed into a matrix Q. Then X is computed by multiplying PT and Q. These two stages of computation are tightly pipelines to form an integrated systolic array which is capable of solving the simultaneous linear equations in just 6n + m – 2 time steps. This systolic array achieves maximum data pipelining rate and its computation time, in a sense, is optimal.

Received July 1987. revised September 1988.

* To whom correspondence should be addressed.

§ Department of Computer Science and Information Engineering, National Taiwan University, Taipei, Taiwan, R.O.C.


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