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At least 289 records · Page 16
All sourcesNASA NTRSDOE OSTI
NASA NTRS1984

Parallel, iterative solution of sparse linear systems: Models and architectures

A model of a general class of asynchronous, iterative solution methods for linear systems is developed. In the model, the system is solved by creating several cooperating tasks that each compute a portion of the solution vector. A data transfer model predicting both the probability that data must be transferred between two tasks and the amount of data to be transferred is presented. This model is used to derive an execution time model for predicting parallel execution time and an optimal number of tasks given the dimension and sparsity of the coefficient matrix and the costs of computation, synchronization, and communication. The suitability of different parallel architectures for solving randomly sparse linear systems is discussed. Based on the complexity of task scheduling, one parallel architecture, based on a broadcast bus, is presented and analyzed.

Reed, D. A.↗
NASA NTRS1984

An inerference assessment approach for a three-dimensional slotted tunnel with sparse wall pressure data

The various procedures referred to as wall interference assessment and correction procedures presume the existence of a surface distribution of data (usually static pressure) measured over a surface on or near the tunnel walls for each test point to be assessed. An alternative approach in which a reasonably sophisticated computer model of the test section flow would be fitted parametrically to a sparse set of measured data is presented. The measurements provides line distributions of static pressure near the center lines of the top, side and bottom walls. The development of a test section model incorporating explicit recognition of discrete slots of finite length with controlled flow reentry into the solid wall downstream portion of the tunnel is shown.

Kemp, W. B., Jr.↗
NASA NTRS1985

Modeling the radiant transfers of sparse vegetation canopies

The scattering dynamics of sparse vegetation canopies were studied within the framework of the three-dimensional radiative transfer model of Kimes (1984). The model was upgraded by including an algorithm for the anisotropic scattering of a soil boundary. Validation of the model was carried out using measured directional reflectance data for two canopies exhibiting typical scattering behavior with low and intermediate vegetation density. The canopies were: an orchard grass canopy; and a hard wheat canopy. A number of factors were found contributing to the final reflectance distribution of the canopies, including: (1) the strong anisotropic scattering properties of the soil; (2) the geometric effect of the vegetation probability gap function on the soil anisotropy and solar irradiance; and (3) the anisotropic scattering of vegetation which is controlled by the phase function and the layering of leaves. The application of the theoretical results to the development of earth-observing sensor systems is discussed.

Kimes, D. S.↗
NASA NTRS1986

Shadowed Space Heating of Sparse Structures

Complete heat-flux and temperature maps computed. Computer program SSQ developed to address and quantify complex, solar-shadowing conditions inherent in sparse, lattice-type space structures. Analysis procedure one of assessing partial shadowing of structural elements by multiple, similar slender members. Program yields schedules of incident-solar, Earth-thermal, and Earth-albedo radiation throughout complete orbit for elemental locations on selected structural members. Thermal response computed in optional routine. Complete heat-flux and temperature mapping obtained by repeated computations for selected elements of interest.

Oneill, J. L.↗
NASA NTRS1985

Multiprocessor sparse L/U decomposition with controlled fill-in

Generation of the maximal compatibles of pivot elements for a class of small sparse matrices is studied. The algorithm involves a binary tree search and has a complexity exponential in the order of the matrix. Different strategies for selection of a set of compatible pivots based on the Markowitz criterion are investigated. The competing issues of parallelism and fill-in generation are studied and results are provided. A technque for obtaining an ordered compatible set directly from the ordered incompatible table is given. This technique generates a set of compatible pivots with the property of generating few fills. A new hueristic algorithm is then proposed that combines the idea of an ordered compatible set with a limited binary tree search to generate several sets of compatible pivots in linear time. Finally, an elimination set to reduce the matrix is selected. Parameters are suggested to obtain a balance between parallelism and fill-ins. Results of applying the proposed algorithms on several large application matrices are presented and analyzed.

Alaghband, G.↗
NASA NTRS1986

A view of Kanerva's sparse distributed memory

Pentti Kanerva is working on a new class of computers, which are called pattern computers. Pattern computers may close the gap between capabilities of biological organisms to recognize and act on patterns (visual, auditory, tactile, or olfactory) and capabilities of modern computers. Combinations of numeric, symbolic, and pattern computers may one day be capable of sustaining robots. The overview of the requirements for a pattern computer, a summary of Kanerva's Sparse Distributed Memory (SDM), and examples of tasks this computer can be expected to perform well are given.

Denning, P. J.↗
NASA NTRS1986

Notes on implementation of sparsely distributed memory

The Sparsely Distributed Memory (SDM) developed by Kanerva is an unconventional memory design with very interesting and desirable properties. The memory works in a manner that is closely related to modern theories of human memory. The SDM model is discussed in terms of its implementation in hardware. Two appendices discuss the unconventional approaches of the SDM: Appendix A treats a resistive circuit for fast, parallel address decoding; and Appendix B treats a systolic array for high throughput read and write operations.

Keeler, J. D.↗
NASA NTRS1986

The application of a sparse, distributed memory to the detection, identification and manipulation of physical objects

To determine the relation of the sparse, distributed memory to other architectures, a broad review of the literature was made. The memory is called a pattern memory because they work with large patterns of features (high-dimensional vectors). A pattern is stored in a pattern memory by distributing it over a large number of storage elements and by superimposing it over other stored patterns. A pattern is retrieved by mathematical or statistical reconstruction from the distributed elements. Three pattern memories are discussed.

Kanerva, P.↗
NASA NTRS1987

Solving very large, sparse linear systems on mesh-connected parallel computers

The implementation of Pan and Reif's Parallel Nested Dissection (PND) algorithm on mesh connected parallel computers is described. This is the first known algorithm that allows very large, sparse linear systems of equations to be solved efficiently in polylog time using a small number of processors. How the processor bound of PND can be matched to the number of processors available on a given parallel computer by slowing down the algorithm by constant factors is described. Also, for the important class of problems where G(A) is a grid graph, a unique memory mapping that reduces the inter-processor communication requirements of PND to those that can be executed on mesh connected parallel machines is detailed. A description of an implementation on the Goodyear Massively Parallel Processor (MPP), located at Goddard is given. Also, a detailed discussion of data mappings and performance issues is given.

Opsahl, Torstein↗
NASA NTRS1987

Two demonstrators and a simulator for a sparse, distributed memory

Described are two programs demonstrating different aspects of Kanerva's Sparse, Distributed Memory (SDM). These programs run on Sun 3 workstations, one using color, and have straightforward graphically oriented user interfaces and graphical output. Presented are descriptions of the programs, how to use them, and what they show. Additionally, this paper describes the software simulator behind each program.

Brown, Robert L.↗
NASA NTRS1986

Comparison between sparsely distributed memory and Hopfield-type neural network models

The Sparsely Distributed Memory (SDM) model (Kanerva, 1984) is compared to Hopfield-type neural-network models. A mathematical framework for comparing the two is developed, and the capacity of each model is investigated. The capacity of the SDM can be increased independently of the dimension of the stored vectors, whereas the Hopfield capacity is limited to a fraction of this dimension. However, the total number of stored bits per matrix element is the same in the two models, as well as for extended models with higher order interactions. The models are also compared in their ability to store sequences of patterns. The SDM is extended to include time delays so that contextual information can be used to cover sequences. Finally, it is shown how a generalization of the SDM allows storage of correlated input pattern vectors.

Keeler, James D.↗
NASA NTRS1987

Strategies for vectorizing the sparse matrix vector product on the CRAY XMP, CRAY 2, and CYBER 205

Large, randomly sparse matrix vector products are important in a number of applications in computational chemistry, such as matrix diagonalization and the solution of simultaneous equations. Vectorization of this process is considered for the CRAY XMP, CRAY 2, and CYBER 205, using a matrix of dimension of 20,000 with from 1 percent to 6 percent nonzeros. Efficient scatter/gather capabilities add coding flexibility and yield significant improvements in performance. For the CYBER 205, it is shown that minor changes in the IO can reduce the CPU time by a factor of 50. Similar changes in the CRAY codes make a far smaller improvement.

Bauschlicher, Charles W., Jr.↗
NASA NTRS1988

Two alternate proofs of Wang's lune formula for sparse distributed memory and an integral approximation

In Kanerva's Sparse Distributed Memory, writing to and reading from the memory are done in relation to spheres in an n-dimensional binary vector space. Thus it is important to know how many points are in the intersection of two spheres in this space. Two proofs are given of Wang's formula for spheres of unequal radii, and an integral approximation for the intersection in this case.

Jaeckel, Louis A.↗
NASA NTRS1988

Using data tagging to improve the performance of Kanerva's sparse distributed memory

The standard formulation of Kanerva's sparse distributed memory (SDM) involves the selection of a large number of data storage locations, followed by averaging the data contained in those locations to reconstruct the stored data. A variant of this model is discussed, in which the predominant pattern is the focus of reconstruction. First, one architecture is proposed which returns the predominant pattern rather than the average pattern. However, this model will require too much storage for most uses. Next, a hybrid model is proposed, called tagged SDM, which approximates the results of the predominant pattern machine, but is nearly as efficient as Kanerva's original formulation. Finally, some experimental results are shown which confirm that significant improvements in the recall capability of SDM can be achieved using the tagged architecture.

Rogers, David↗
NASA NTRS1988

Sparse distributed memory prototype: Principles of operation

Sparse distributed memory is a generalized random access memory (RAM) for long binary words. Such words can be written into and read from the memory, and they can be used to address the memory. The main attribute of the memory is sensitivity to similarity, meaning that a word can be read back not only by giving the original right address but also by giving one close to it as measured by the Hamming distance between addresses. Large memories of this kind are expected to have wide use in speech and scene analysis, in signal detection and verification, and in adaptive control of automated equipment. The memory can be realized as a simple, massively parallel computer. Digital technology has reached a point where building large memories is becoming practical. The research is aimed at resolving major design issues that have to be faced in building the memories. The design of a prototype memory with 256-bit addresses and from 8K to 128K locations for 256-bit words is described. A key aspect of the design is extensive use of dynamic RAM and other standard components.

Flynn, Michael J.↗
NASA NTRS1989

Parallel solution of sparse one-dimensional dynamic programming problems

Parallel computation offers the potential for quickly solving large computational problems. However, it is often a non-trivial task to effectively use parallel computers. Solution methods must sometimes be reformulated to exploit parallelism; the reformulations are often more complex than their slower serial counterparts. We illustrate these points by studying the parallelization of sparse one-dimensional dynamic programming problems, those which do not obviously admit substantial parallelization. We propose a new method for parallelizing such problems, develop analytic models which help us to identify problems which parallelize well, and compare the performance of our algorithm with existing algorithms on a multiprocessor.

Nicol, David M.↗
NASA NTRS1990

Two-dimensional shape recognition using sparse distributed memory

Researchers propose a method for recognizing two-dimensional shapes (hand-drawn characters, for example) with an associative memory. The method consists of two stages: first, the image is preprocessed to extract tangents to the contour of the shape; second, the set of tangents is converted to a long bit string for recognition with sparse distributed memory (SDM). SDM provides a simple, massively parallel architecture for an associative memory. Long bit vectors (256 to 1000 bits, for example) serve as both data and addresses to the memory, and patterns are grouped or classified according to similarity in Hamming distance. At the moment, tangents are extracted in a simple manner by progressively blurring the image and then using a Canny-type edge detector (Canny, 1986) to find edges at each stage of blurring. This results in a grid of tangents. While the technique used for obtaining the tangents is at present rather ad hoc, researchers plan to adopt an existing framework for extracting edge orientation information over a variety of resolutions, such as suggested by Watson (1987, 1983), Marr and Hildreth (1980), or Canny (1986).

Kanerva, Pentti↗
NASA NTRS1989

Parallel iterative methods for sparse linear and nonlinear equations

As three-dimensional models are gaining importance, iterative methods will become almost mandatory. Among these, preconditioned Krylov subspace methods have been viewed as the most efficient and reliable, when solving linear as well as nonlinear systems of equations. There has been several different approaches taken to adapt iterative methods for supercomputers. Some of these approaches are discussed and the methods that deal more specifically with general unstructured sparse matrices, such as those arising from finite element methods, are emphasized.

Saad, Youcef↗