Issue No. 05 - May (1993 vol. 42)

ISSN: 0018-9340

pp: 513-517

DOI Bookmark: http://doi.ieeecomputersociety.org/10.1109/12.223670

ABSTRACT

<p>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.</p>

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.

CITATION

S.Y. Berkovich, "An Overlaying Technique for Solving Linear Equations in Real-Time Computing",

*IEEE Transactions on Computers*, vol. 42, no. , pp. 513-517, May 1993, doi:10.1109/12.223670