| Abstract: | Conclusion We have proposed a modification of the orthogonal Faddeev method 6] for solving various SLAE and also for inversion and pseudoinversion
of matrices. The proposed version of the method relies on Householder and Jordan-Gauss methods and its computational complexity
is approximately half that of 6]. This method, combined with the matrix-graph method 9] of formalized SPPC structure design,
has been applied to synthesize a number of AP architectures that efficiently implement the proposed method. Goal-directed
isomorphic and homeomorphic transformations of the LFG of the original algorithm (5) lead to a one-dimensional (linear) AP
of fixed size, with minimum hardware and time costs and with minimized input-output channel width.
The proposed algorithm (5) has been implemented using a 4-processor AP, with Motorola DSP96002 processors as PEs (Fig. 7).
Application of the algorithm (5) to solve an SLAE with a coefficient matrixA withM=N=100 and one righthand side on this AP produced a load factor η=0.82; for inversion of the matrixA of the same size we achieved η=0.77.
The sequence of transformations and the partitioning of a trapezoidal planaer LFG described in this article have been generalized
to the case of other LA algorithms decribed by triangular planar LFGs and executed on linear APs. It is shown that the AP
structures synthesized in this study execute all the above-listed algorithms no less efficiently than the modified Faddeev
algorithm, provided their PEs are initially tuned to the execution of the corresponding operators.
Translated from Kibernetika i Sistemnyi Analiz, No. 2, pp. 47–66, March–April, 1996. |
