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An Overlaying Technique for Solving Linear Equations in Real-Time Computing
May 1993 (vol. 42 no. 5)
pp. 513-517

A computer organization for solving a continuous stream of sets of linear equations A*b with relatively close consecutive parameters is described. The conditions of closeness enabling this technique are monitored during the computations. The cycles of the computational process are divided into two stages: finding a solution of a current set of linear equations by multiplying components of a polynomial approximation of the inverse matrix by a right-hand-side vector; and calculating this inverse matrix in order to arrange for an approximation of the next inverse matrix. The former procedure can be performed in O(n/sup 2/) operations, reducing the time for obtaining the solution of linear equations. The more lengthy calculation of the inverse itself, which requires O(n/sup 3/) operations, can overlay the preparation of the upcoming set of equations in the next cycle. The approach can be effectively utilized for organization of real-time computations.

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Index Terms:
overlaying technique; real-time computing; computer organization; linear equations; close consecutive parameters; computational process; polynomial approximation; inverse matrix; real-time computations; computational complexity; matrix algebra; real-time systems.
S.Y. Berkovich, "An Overlaying Technique for Solving Linear Equations in Real-Time Computing," IEEE Transactions on Computers, vol. 42, no. 5, pp. 513-517, May 1993, doi:10.1109/12.223670
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