Showing papers on "Computation published in 1981"

The cube-connected cycles: a versatile network for parallel computation

Abstract: An interconnection pattern of processing elements, the cube-connected cycles (CCC), is introduced which can be used as a general purpose parallel processor. Because its design complies with present technological constraints, the CCC can also be used in the layout of many specialized large scale integrated circuits (VLSI). By combining the principles of parallelism and pipelining, the CCC can emulate the cube-connected machine and the shuffle-exchange network with no significant degradation of performance but with a more compact structure. We describe in detail how to program the CCC for efficiently solving a large class of problems that include Fast Fourier transform, sorting, permutations, and derived algorithms.

Automatic Differentiation: Techniques and Applications

Abstract: Formula translation.- Formula differentiation.- Generation of Taylor coefficients.- Examples of software for automatic differentiation and generation of Taylor coefficients.- Automatic computation of gradients, Jacobians, Hessians, and applications to optimization.- Automatic error analysis.- Solution of nonlinear systems of equations.- Numerical integration with regorous error estimation.- Additional notes of techniques, applications, and software.

Direct mapping of seismic data to the domain of intercept time and ray parameter—A plane‐wave decomposition

Abstract: Marine seismic data recorded as a function of source‐receiver offset and traveltime are mapped directly to the domain of intercept or vertical delay time and horizontal ray parameter. This is a plane‐wave decomposition based on beam forming of wide‐aperture seismic array data to determine automatically the loci of coherent seismic reflection and refraction events. In this computation, semblance, in addition to the required slowness or horizontal ray parameter stack, is found for linear X — T trajectories across subarrays. Subsequently, semblance is used to derive a windowing filter that is applied to the slowness stack to determine the points of stationary phase and eliminate aliasing. The resulting filtered slowness stacks for multiple subarrays can then be linearly transformed and combined according to ray parameter, range, and time. The resulting function of intercept time and horizontal ray parameter offers significant computational and interpretational advantages for the case of horizontal homogeneou...

Distributed dynamic programming

Abstract: We consider distributed algorithms for solving dynamic programming problems whereby several processors participate simultaneously in the computation while maintaining coordination by information exchange via communication links. A model of asynchronous distributed computation is developed which requires very weak assumptions on the ordering of computations, the timing of information exchange, the amount of local information needed at each computation node, and the initial conditions for the algorithm. The class of problems considered is very broad and includes shortest path problems, and finite and infinite horizon stochastic optimal control problems. When specialized to a shortest path problem the algorithm reduces to the algorithm originally implemented for routing of messages in the ARPANET.

On the design of high performance digital arithmetic units

Abstract: Several new algorithms for use for enhancing the performance of pipelined digital computers have been developed and evaluated. The design of a particular such computer embodying most of these algorithms is discussed in detail--the S-1 Mark IIA. The relationship and importance of the new algorithms to the overall performance of such a machine is analyzed. An algorithm for the very rapid pipelined computation of medium precision approximations (about 30 bits for the Mark IIA) to elementary functions is described. This method uses table lookup and two parallel multiplications to triple the precision available from direct table lookup. Current RAM technology permits the effective use of this algorithm for non-trivial word sizes. The method is applied to reciprocal, square-root, exponential, logarithm, arctangent, sine, cosine, and the error function. A floating-point addition algorithm which has a much shorter latency than previous approaches is developed and analyzed. This algorithm lends itself to the efficient simultaneous calculation of floating-point sums and differences, which is of great value computing FFTs and to other related algorithms. The algorithm resolves floating-point addition into one of two independent cases, each of which can be implemented in fewer logic gate delays than previous algorithms. Previous techniques of sorting on pipelined machines are analyzed and a new algorithm based on Quicksort is developed. This new algorithm is significantly faster and simpler than previous pipelined sorting techniques. The use of skewed data representations to increase the performance of interleaved memories for many algorithms is well known. However a large price is paid in convenience by the use of such techniques. A new approach which allows the use of normal data representations but which has all of the performance advantages of the skewed representations is described. This technique is particularly valuable since the hardware used to implement it can also serve as a queue to minimize the effects of temporary stoppages in the instruction and operand fetching and arithmetic execution hardware. Several other new techniques for performance enhancement are also described and analyzed, and fruitful directions for future work in this area are discussed.

A numerical inversion of the laplace transform solution to radial dispersion in a porous medium

Abstract: A special form of the numerical inversion of the Laplace transform described by Stehfest (1970) is applied to the transformed solution of dispersion in a radial flow system in a porous medium. The inversion is extremely simple to use because the weighting coefficients depend only on the number of terms used in the computation and not upon the transform solution as required by most numerical inversion techniques. The result obtained by use of this approximate inversion of the radial dispersion problem reproduced the curves obtained previously by Hoopes and Harleman (1967) with a finite difference scheme.

A Simple but Realistic Model of Floating-Point Computation

Abstract: A model of floating-point computation, intended as a basis for efficient portable mathematical software, is presented. The model involves only simple familiar concepts, expressed in a small set of environment parameters. Using these, both a program and its documentation can tailor themselves to the host computer. First, the model numbers, a conventional four-parameter system of floating-point numbers, are introduced. The parameters are the base, the precision, and the minimum and maximum exponents. They must be chosen so that the result of a basic arithmetic operation on model numbers is no less accurate than the result that would be obtained by chopped arithmetic in the model system. Also, the result of a basic operation on operands between model numbers must be bounded by the results of the same operation on the neighboring model numbers. These ideas are summarized in a few fundamental axioms, which enable the machine-independent properties of numerical programs to be stated and proved. The main conclusion is that the model supports conventional, worst case, forward or backward error analyses with only minor qualifications. The model is simple in the sense that its axioms are more easily stated and understood than the detailed operational rules of most floating-point processors. It is realistic in the sense that real computers exhibit most of the forms of behavior (or misbehavior) that it allows, but nearly always conform to its rules.

Representation of Multivalued Functions Using the Direct Cover Method

Abstract: An efficient method for representing multivalued functions is described. The method employs an algorithm which generates an efficient cover for a given function "directly," i.e., without resorting to the intermediate step of creating a table of prime implicants. Data are presented to show that the covers generated are as efficient in terms of cover size as prime implicant based methods. More importantly, however, the direct cover method is shown to require much less computation time than prime implicant based methods, thus making it practical for functions with a large number of input variables and/or as the radix of implementation increases. The algorithm is introduced by applying it to functional representations employing the traditional max and min operation. Next, a modified form of the algorithm is presented for use with the sum and product operators more appropriate to I2L and other current summation technologies.

The octahedral algorithm, a new simplicial fixed point algorithm

Abstract: A new variable dimension simplicial algorithm for the computation of solutions of systems of nonlinear equations or the computation of fixed points is presented. It uses the restrart technique of Merrill to improve the accuracy of the solution. The algorithm is shown to converge quadratically under certain conditions. The algorithm should be efficient and relatively easy to implement.

A Critique and an Appraisal of VLSI Models of Computation.

Abstract: Considerable attention has been paid to the definition of a suitable model of computation for Very-Large-Scale Integrated (VLSI) circuits [1], [2], [3], [4]. The basic parameters of any VLSI computation model are chip area A and computation time T. VLSI systems display a trade-off between these two parameters, each of which represents a well-defined cost aspect: chip area is a measure of fabrication cost and computation time is a measure of operating cost. VLSI Models of Computation

A Parametric Linear Complementarity Technique for the Computation of Equilibrium Prices in a Single Commodity Spatial Model.

Abstract: This paper presents a parametric linear complementarity technique for the computation of equilibrium prices in a single commodity spatial model We first reformulate the model as a linear complementarity problem and then apply the parametric principal pivoting algorithm for its solution This reformulation leads to the study of an “arc—arc weighted adjacency matrix” associated with a simple digraph having weights on the nodes Several basic properties of such a matrix are derived Using these properties, we show how the parametric principal pivoting algorithm can be greatly simplified in this application Finally, we report some computational experience with the proposed technique for solving some large problems

Power System Security Corridors Concept and Computation

Abstract: This paper introduces a novel scheme for the region-wise predictive security assessment. The proposed scheme is based on the concept of the security corridor, which assumes that the normal range of operating points can be restricted to the neighborhood of the system's predicted (or nominal) trajectory. Our scheme tries to characterize this neighborhood by a number of ellipsoids overlapping along the system's predicted trajectory. The intersection of these ellipsoids with the system's steady-state security region defines a security corridor which is characterizable by a relatively small number of constraints. Each ellipsoid covers a specific operating time interval, so the time of operation serves as a localizing parameter in this scheme. The small number of constraints needed to describe the secure part of an ellipsoid allows the efficient use of the security corridors in a variety of power system operation and planning applications. For on-line security monitoring, for instance, as long as the actual trajectory stays within the "width" of the security corridor - which can be verified rather trivially - the system security is guaranteed. The effort involved in constructing a security corridor is explained through a discussion on some computational aspects of the scheme, and by presenting the results of some numerical studies performed on a sample system.

Computation of separated flows by a vortex-tracing algorithm

Abstract: Numerical solutions for two-dimensional, time-dependent, separated flows around bodies are obtained, using a new version of the vortex method. This method provides an efficient representation of flows involving large regions of separation. The modifications incorporated in the new version, which improve its accuracy, versatility, and computing speed, are described. The computer cost is only of the order of the 3/2 power on N, instead of N-squared, for each step with N vortices. Arbitrary shapes can be treated; a conformal mapping is not required. Special attention is paid to the viscous character of the solution and to the accurate computation of the pressure distribution at the body surface. The vortex solution for the outer flow is coupled to an inner solution for the attached part of the boundary layer. Numerical results are presented for several bluff bodies exhibiting dependence on Reynolds number, for stationary airfoils under steady or transient conditions and for oscillating airfoils, including dynamic stalls. These results are compared with other available results, analytical or experimental, and demonstrate the enhanced reliability and accuracy of the improved method.

Line/Polygon Classification: A Study of the Complexity of Geometric Computation

Abstract: Illuminating the techniques of computational geometry, an analysis of two LPC algorithms compares their efficiency for handling polygon-clipping problems.

On relations between input and communication/computation in VLSI

Abstract: This extended abstract examines some of the fundamental issues involved. It is shown that when multiple copies of the inputs are allowed the standard methodology for deriving lower bounds on the complexity of VLSI chips is no longer applicable. A simple example is presented whose upper bound complexity with mUltiple copies of the inputs is below the lower bound complexity of that function when only a single copy of the inputs upper and lower bounds on such complexity for certain functions or families of functions. An important assumption made in the cited literature is that the inputs to the computations are made available to the chip only once. While this assumption is not of significance in the context of classical algorithm design for random access machines, it may carry important implications in the context of VLSI, where providing several copies of the inputs may be successfully employed to reduce the complexity of the computation. have is allowed. Finally, lower bounds on the complexity of a family of functions are derived for the case when multiple copies of the inputs are permitted.

Computation of the electric potential in three‐dimensional structures*

Abstract: A method has been developed for computation of the electrical DC potential of an arbitrary three-dimensional resistivity structure using a finite difference method. The threedimensionality is necessary for interpretation of geoelectrical soundings with controlled point sources over a laterally inhomogeneous medium. Lateral inhomogeneities should be considered in resistivity soundings with large layouts. The results obtained with the described method permit a more realistic representation of geological features. The resolution of the method is determined by the number of elements in the resistivity network. The problem of core memory space has been resolved by using random access disc files. The results computed using a Fortran program are in good agreement with analytically obtained solutions.

Algorithm 45. Automatic computation of improper integrals over a bounded or unbounded planar region

Abstract: An automatic quadrature algorithm especially designed for double integration of functions with some form of singular behaviour on the boundary of the integration region is described, and its FORTRAN code is presented.

Computation of correlation sequences in two-dimensional digital filters

Abstract: Two approaches to the computation of correlations or variances in 2-D digital filters are presented. The first one establishes the correlation equations and shows that the equations are consistent for the special cases of one-dimensional (1-D) filters and 2-D symmetric filters. The second one is a direct application of the theory of 2-D complex integrals, whereby the first of the two integrations becomes a Euclid problem and the second becomes a 1-D complex integration problem. This second method is applicable to general 2-D digital filters.

Pattern recognition system operating by the multiple similarity method

Abstract: A plurality of pattern similarity computation circuits (24, to 24n) are provided, and different sample pattern data and a reference pattern data are coupled to the individual computation circuits, whereby the calculation of the similarity degree of the reference pattern with respect to the individual sample patterns is simultaneously made in the respective computation circuits (241 to 24n).

Complexity of algorithms and computations

Abstract: A survey is given of some results on the complexity of algorithms and computations published up to 1973.

Measures of parallelism in alternating computation trees (Extended Abstract)

Abstract: We examine three ways of restricting the size (and shape) of the accepting computation trees of alternating Turing machines. We continue study by examining bounds on the number of leaves in the tree (Section 3), the 'width' of the tree (Section 4), and the number of nodes at any level of the tree (Section 5). Each of these measures can be interpreted as a limit on the amount of parallelism permitted the computation.

Higher Approximation of Steady Oscillations in Nonlinear Systems with Single Degree of Freedom : Suggested Multi-Harmonic Balance Method

Abstract: In order to obtain the higher order approximate solutions for steady oscillations of a nonlinear system, a so-called multi-harmonic balance method is suggested, for computing a number of harmonic components simultaneously. The formalization of the computation in the successive approximation is devised by applying the complex Fourier series and the general and detailed procedure is indicated clearly. Using as an example the homogeneous Duffing equation, for which an exact solution is known, the accuracy and the mechanism by which the computational errors occur are discussed. The method is fully examined generally and with regard to the technique of machine computation.