An Instruction Systolic Array which is capable of executing a small set of one and two operand instructions for comparing and exchanging data items of adjacent processors is presented. Typical ISA programs for searchi...
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An Instruction Systolic Array which is capable of executing a small set of one and two operand instructions for comparing and exchanging data items of adjacent processors is presented. Typical ISA programs for searching and sorting algorithms are included.
In this paper a group explicit method is introduced for the first order convection equation. The stability analysis confirms the method to be neutrally stable with convergence of 0(Delta x) + 0(Delta t(2)).
In this paper a group explicit method is introduced for the first order convection equation. The stability analysis confirms the method to be neutrally stable with convergence of 0(Delta x) + 0(Delta t(2)).
Modern electronic systems especially sensor and imaging systems, are beginning to incorporate their own neural network sub-systems. In order for these neural systems to learn in real-time they must be implemented usin...
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Modern electronic systems especially sensor and imaging systems, are beginning to incorporate their own neural network sub-systems. In order for these neural systems to learn in real-time they must be implemented using VLSI technology, with as much of the learning processes incorporated on-chip as is possible. Most VLSI implementations literally implement a series of neural processing cells, which can be connected together in an arbitrary fashion. The work presented here utilises two-dimensional instruction systolic arrays in an attempt to define a general neural architecture which is closer to the biological basis of neural networks-it is the synapses themselves, rather than the neurons, that have dedicated processing units. The architecture has been defined, along with a limited instruction set, and has been shown to operate correctly under simulation for the backpropagation training algorithm.
In this paper a new explicit alternating direction (EAD) method is presented for the numerical solution of partial differential equations in 2 and 3 dimensions. It is shown that the method is stable and comparable in ...
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In this paper a new explicit alternating direction (EAD) method is presented for the numerical solution of partial differential equations in 2 and 3 dimensions. It is shown that the method is stable and comparable in accuracy to the established ADI methods. Finally the new method because of its 'explicitness' is ideally suitable for massively parallel computers.
A cyclic reduction method is described for the fast numerical solution of constant tridiagonal Toeplitz linear systems which occur repeatedly in the solution of the implicit finite difference equations derived from li...
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A cyclic reduction method is described for the fast numerical solution of constant tridiagonal Toeplitz linear systems which occur repeatedly in the solution of the implicit finite difference equations derived from linear first order hyperbolic equations, i.e. the Transport equation, under a variety of boundary conditions. In this paper, we show that the linear systems can be solved efficiently by the Stride of 3 reduction algorithm.
A new 4th order Runge-Kutta method for solving initial value problems is derived by replacing the arithmetic means in the formulawhereetc., by their geometric means ***. to yield initially a low order accuracy formula...
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A new 4th order Runge-Kutta method for solving initial value problems is derived by replacing the arithmetic means in the formulawhereetc., by their geometric means ***. to yield initially a low order accuracy formula. However by re-comparing the Taylor series expansions ofk1k2k3andk4in terms of the functional derivatives and theαijparameters, a fourth order accuracy formula is obtained which is confirmed by numerical experiments. Then, a new fourth order Runge-Kutta method for solving linear initial value problems of the formy′ =Ayis derived which provides an estimate of the truncation error without any extra function evaluations. The idea follows from the fact that two numerical solutions of similar order can be obtained by using the arithmetic mean (AM) and the geometric mean (GM) averaging of the functional values. The numerical results given confirm that this new method is suitable to be used as an error control strategy.
In this paper, the recently introduced Alternating Group Explicit (AGE) method is compared with the well-known Successive Overrelaxation (SOR) methods. Both theoretical and experimental results confirm that the two me...
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In this paper, the recently introduced Alternating Group Explicit (AGE) method is compared with the well-known Successive Overrelaxation (SOR) methods. Both theoretical and experimental results confirm that the two methods have similar convergence rates. Copyright (C) 1996 Published by Elsevier Science Limited.
In this paper, the parallel solution of the P-cyclic matrix system derived from the finite difference/element discretisation of the two point boundary-value problem is developed although the P-cyclic system also arise...
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In this paper, the parallel solution of the P-cyclic matrix system derived from the finite difference/element discretisation of the two point boundary-value problem is developed although the P-cyclic system also arises in many other stochastic applications. The direct solution by the Gaussion elimination method is developed into an algorithmic procedure which is used for solving the P-cyclic system. A parallel architecture is then designed based on the algorithm to speedup the solution. The architecture employs a systolic array, which comprises a triangular systolic array and a rectangular systolic array, to perform the block triangularisation of the P-cyclic system. The block triangular system is solved by a local memory system in parallel. The results show that when the order of the differential equation is larger than 10, the speedup of the parallel system is significant. The efficiency of the architecture can be up to more than 50%.
In this paper, we introduce a new approach to the solution of linear systems of equations which have the form of AX + XB = C. Such systems arise from finite difference discretizations of separable elliptic boundary va...
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In this paper, we introduce a new approach to the solution of linear systems of equations which have the form of AX + XB = C. Such systems arise from finite difference discretizations of separable elliptic boundary value problems on rectangular domains. They also occur in applications in control theory. The conjugate gradient (CG) method for solving such systems is presented. The preconditioned conjugate gradient (PCG) method is also developed with both an n x n block diagonal preconditioner and a new block 2n x 2n diagonal preconditioner. Both the CG method and the PCG methods are applied to the Poisson model problems and the rates of convergence of these methods are compared via numerical experiments.
This paper deals with the theoretical aspects of the Generalized Conjugate Gradient (GCG) method of Concus and Golub (1976) and Widlund (1978) applied to the least squares problems (LSP). The connections with the CG a...
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This paper deals with the theoretical aspects of the Generalized Conjugate Gradient (GCG) method of Concus and Golub (1976) and Widlund (1978) applied to the least squares problems (LSP). The connections with the CG algorithms are given. Thereby the convergence bound given by Eisenstat (1982) is improved in some cases. The AGCG algorithms I and II are developed, which are an adjusted form of the GCG method depending on the initial choice and take approximately half of the work per iteration of the GCG. New stopping criteria are given for the GCG (and AGCG) method. The absolute error stopping criterion is proved theoretically and shown numerically to be better than that suggested by Widlund (1978).
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