36271721
Industrial Application Areas of High-Performance Computing
In 1993, a list of the top 500 supercomputer sites worldwide was made available for the first time. Since then, the Top500 list has been published twice a year. The list allows a detailed and well-founded analysis of the state of high-performance computing (HPC). This article summarizes the recent trends in application areas of HPC systems, focusing on the increase in industrial installations and applications.
17421545
Recent trends in the marketplace of high performance computing
In this paper we analyze major recent trends and changes in the High Performance Computing (HPC) market place. The introduction of vector computers started the area of 'Supercomputing'. The initial success of vector computers in the seventies was driven by raw performance. Massive parallel systems (MPP) became successful in the early nineties due to their better price/performance ratios, which was enabled by the attack of the 'killer-micros'. The success of microprocessor based on the shared memory concept (referred to as symmetric multiprocessors (SMP)) even for the very high-end systems, was the basis for the emerging cluster concepts in the early 2000s. Within the first half of this decade clusters of PC's and workstations have become the prevalent architecture for many HPC application areas on all ranges of performance. However, the Earth Simulator vector system demonstrated that many scientific applications could benefit greatly from other computer architectures. At the same time there is renewed broad interest in the scientific HPC community for new hardware architectures and new programming paradigms. The IBM BlueGene/L system is one early example of a shifting design focus for large-scale system. The DARPA HPCS program has the declared goal of building a Petaflops computer system by the end of the decade using novel computer architectures.
35264400
Parallel Efficiency of the Lanczos Method for Eigenvalue Problems
LBNL-42828 Parallel Efficiency of the Lanczos Method for Eigenvalue Problems ^ Kesheng Wu+and Horst Simon* Abstract Two of the commonly used versions of the Lanczos method for eigenvalues problems are the shift-and-invert Lanczos method and the restarted Lanczos method. In this talk, we will address two questions, is the shift-and-invert Lanczos method a viable option on massively parallel machines and which one is more appropriate for a given eigenvalue problem? Introduction T h i s talk is o n how to compute eigenvalues a n d eigenvectors of large sparse s y m m e t r i c matrices o n massively parallel machines. One of the the most c o m m o n l y used algorithms for this task is the Lanczos m e t h o d w h i c h projects the large eigenvalue p r o b l e m onto a low dimensional K r y l o v subspace [7, 10]. I n most cases, the K r y l o v subspace basis is built t h r o u g h a series of matrix-vector m u l t i p l i c a t i o n s , the whole Lanczos m e t h o d c a n be implemented w i t h a matrix-vector m u l t i p l i c a t i o n routine a n d a few simple vector operations. T h i s a l g o r i t h m is highly efficient on parallel machines a n d it is effective for c o m p u t i n g extreme a n d well separated eigenvalues. To compute the interior or not well-separated eigenvalues, the shift-and-invert Lanczos m e t h o d is one of the most effective methods. Since the eigenvalues of a m a t r i x A are related to the eigenvalues of (A — c r l ) by a simple relation X(A) = a + 1/X((A — c r l ) ) a n d the corresponding eigenvectors of A a n d (A — c r l ) are identical, the shift-and-invert scheme computes the extreme eigenvalues of (A — c r l ) a n d deduce the corresponding eigenvalues of A. W i t h appropriate choice of a, the extreme eigenvalues of (A — al)^ are well separated and can be easily computed. T h e shift-and-invert Lanczos m e t h o d needs to b u i l d a K r y l o v subspace basis of (A — c r l ) w h i c h is done by solving a series of linear systems involving the coefficient m a t r i x (A — a I). T h e linear systems need to be solved accurately a n d the only reliable means to accomplish this is by using a direct m e t h o d [5]. Because it is difficult to implement direct methods o n d i s t r i b u t e d parallel computers, efficient parallel i m p l e m e n t a t i o n has not been widely available u n t i l recently [1, 8]. T h i s talk w i l l present our s t u d y of the parallel efficiency of the shift-and-invert Lanczos m e t h o d using these newly available direct solvers. T h e study w i l l show that the shift-and-invert Lanczos m e t h o d is ' T h i s w o r k was s u p p o r t e d b y t h e D i r e c t o r , Office o f E n e r g y R e s e a r c h , Office o f L a b o r a t o r y P o l i c y a n d Infrastructure M a n a g e m e n t , of the U . S . D e p a r t m e n t of E n e r g y under C o n t r a c t N o . D E - A C 0 3 - 7 6 S F 0 0 0 9 8 . T h i s r e s e a r c h u s e d r e s o u r c e s o f t h e N a t i o n a l E n e r g y R e s e a r c h S c i e n t i f i c C o m p u t i n g C e n t e r , w h i c h is s u p p o r t e d b y t h e Office o f E n e r g y R e s e a r c h o f t h e U . S . D e p a r t m e n t o f E n e r g y . 'Lawrence Berkeley National Laboratory/NERSC, Berkeley, CA Email: {ksni, hdsimon}81bl.gov.
38908855
Large-Scale SVD and Subspace-Based Methods for Information Retrieval
A theoretical foundation for latent semantic indexing (LSI) is proposed by adapting a model first used in array signal processing to the context of information retrieval using the concept of subspaces. It is shown that this subspace-based model coupled with minimal description length (MDL) principle leads to a statistical test to determine the dimensions of the latent-concept subspaces in LSI. The effect of weighting on the choice of the optimal dimensions of latent-concept subspaces is illustrated. It is also shown that the model imposes a so-called low-rank-plus-shift structure that is approximately satisfied by the cross-product of the term-document matrices. This structure can be exploited to give a more accurate updating scheme for LSI and to correct some of the misconception about the achievable retrieval accuracy in LSI updating. Variants of Lanczos algorithms are illustrated with numerical test results on Cray T3E using document collections generated from World Wide Web.
9150119
Thick-Restart Lanczos Method for Symmetric Eigenvalue Problems
This paper describes a restarted Lanczos algorithm that particularly suitable for implementation on distributed machines. The only communication operation is requires outside of the matrix-vector multiplication is a global sum. For most large eigenvalue problems, the global sum operation takes a small fraction of the total execution time. The majority of the computer is spent in the matrix-vector multiplication. Efficient parallel matrix-vector multiplication routines can be found in many parallel sparse matrix packages such as AZTEC [9], BLOCK-SOLVE [10], PETSc [3], P_SPARSLIB. For this reason, our main emphasis in this paper is to demonstrate the correctness and the effectiveness of the new algorithm.
62731399
NAS parallel benchmark results
The NAS (Numerical Aerodynamic Simulation) parallel benchmarks have been developed at NASA Ames Research Center to study the performance of parallel supercomputer. The eight benchmark problems are specified in a 'pencil and paper' fashion. The performance results of various systems using the NAS parallel benchmarks are presented. These results represent the best results that have been reported to the authors for the specific systems listed. They represent implementation efforts performed by personnel in both the NAS Applied Research Branch of NASA Ames Research Center and in other organizations.<<ETX>>
206567160
Special Feature: Prometheus or Pandora: The Influence of Automation on Society
Even though computer technology may challenge one of man's last and most cherished illusions—that he alone is capable of thought—it can also show him how to live in harmony with nature.
6846387
Causality and Model Abstraction
Abstract Much of science and engineering is concerned with characterizing processes by equations describing the relations that hold among parameters of objects and govern their behavior over time. In formal descriptions of processes in terms of parameters and equations, the notion of causality is rarely made explicit. Formal treatments of the foundations of sciences have avoided discussions of causation and spoken only of functional relations among variables. Nevertheless, the notion of causality plays an important role in our understanding of phenomena. Even when we describe the behavior of a system formally in terms of acausal, mathematical relations, we often give an informal, intuitive explanation of why the system behaves the way it does in terms of cause-effect relations. In this paper, we will present an operational definition of causal ordering. The definition allows us to extract causal dependency relations among variables implicit in a model of a system, when a model is represented as a set of acausal, mathematical relations. Our approach is based on the theory of causal ordering first presented by Simon [22]. The paper shows how to use the theory and its extension in reasoning about physical systems. Further, the paper studies the relation of the theory to the problems of model aggregation.
7797628
Bayesian Networks and Inner Product Spaces
In connection with two-label classification tasks over the Boolean domain, we consider the possibility to combine the key advantages of Bayesian networks and of kernel-based learning systems. This leads us to the basic question whether the class of decision functions induced by a given Bayesian network can be represented within a low-dimensional inner product space. For Bayesian networks with an explicitly given (full or reduced) parameter collection, we show that the “natural” inner product space has the smallest possible dimension up to factor 2 (even up to an additive term 1 in many cases). For a slight modification of the so-called logistic autoregressive Bayesian network with n nodes, we show that every sufficiently expressive inner product space has dimension at least 2 n/4. The main technical contribution of our work consists in uncovering combinatorial and algebraic structures within Bayesian networks such that known techniques for proving lower bounds on the dimension of inner product spaces can be brought into play.
5520100
The Theory of Problem Solving
It is now about fifteen years since the first computer programs were written and tested that used the method of heuristic search to solve problems. Dozens of such programs, some designed for specific task domains, others claiming various degrees of generality, have now been described in the literature, and many experiments with their performance have been reported and analysed. It is an appropriate time to ask what has been learned from these experiments about the general theory of problem solving, and to try to summarize the present state of that theory.
16971158
Laboratory Replication of Scientific Discovery Processes
Fourteen subjects were tape-recorded while they undertook to find a law to summarize numerical doto they were given. The source of the data was not identified, nor were the variables lobeled semantically. Unknown to the subjects. the data were measurements of the distances of the planets from the sun and the periods of their revolutions obout it-equivalent to the doto used by Johonnes Kepler to discover his third low of planetary motion. Four of the 14 subjects discovered the some low as Kepler did (the period varies OS the 3/2 power of the distance), and a fifth come very close to the answer. The subiects’ protocols provide a detatled picture of the problem-solving searches they engoged in, which were mainly, but not exclusively, in the space of possible functions for fitting the data. and provide explanations OS to why some succeeded and the others foiled. The scorch heuristics used by the subjects ore similar to those embodied in the BACON program, a computer simulation of certain scientific discovery processes. The experiment demonstrates the feasibility of examining some of the processes of scientific discovery by recreating, in the laboratory, discovery situations of substontiol historical relevance. It demonstrates also. that under conditions rather similar to those of the originol discoverer, a low can be rediscovered by persons of ordinory intelligence (i.e., the intelligence needed for academic success in a good university). The data for the successful subjects reveal no “creative” processes in this kind of o discovery situation different from those that are regulorly observed in all kinds of problem-solving settings.