In a number of applications, data may be anonymized, obfuscated, or highly noisy. In such cases, it is difficult to use domain knowledge or low-dimensional visualizations to engineer the features for tasks such as machine learning, instead, we explore dimensionality reduction (DR) as a data-driven approach for engineering these low-dimensional representations. Through a careful examination of available feature selection and feature extraction techniques, we propose a new class named feature clustering. These new methods could utilize different forms of clustering to help evaluate the relative importance of features and take on properties different from the well-known DR algorithms. To evaluate these algorithms, we develop a parallel computing framework that optimizes their hyperparameters on a sample of application datasets. This framework harnesses the parallel computing power to examine a large number of parameter combinations and enables hyperparameter tuning and model tuning purely based on observed performance. This optimization framework provides mechanism for users to control computational cost and is able to examine many parameter choices in seconds. On a set of building energy data where the key features are known based on domain knowledge, the optimized DR algorithms indeed identify the expected main drivers of building electricity usage: outdoor temperature and solar radiance. This shows the automated optimization procedure is able to find known features. In terms of modeling accuracy, a distance correlation-based feature clustering method outperforms other DR algorithms including the well-known KPCA, LLE, and UMAP on two different tests.

Electricity is a vital part of our daily life; therefore it is important to avoid irregularities such as the California Electricity Crisis of 2000 and 2001. In this work, we seek to predict anomalies using advanced machine learning algorithms, more specifically a Change Point Detection (CPD) algorithm on the electricity prices during the California Electricity Crisis. Such algorithms are effective, but computationally expensive when applied on a large amount of data. To address this challenge, we accelerate the Gaussian Process (GP) for 1-dimensional time series data. Since GP is at the core of many statistical learning techniques, this improvement could benefit many algorithms. In the specific Change Point Detection algorithm used in this study, we reduce the overall computational complexity from O(n5) to O(n2), where the amountized cost of solving a GP projet is O(1). Our efficient algorithm makes it possible to compute the Change Points using the hourly price data during the California Electricity Crisis. By comparing the detected Change Points with known events, we show that the Change Point Detection algorithm is indeed effective in detecting signals preceding major events.

Two-point Correlation Function (TPCF) is widely used in astronomy to characterize the distribution of matter/energy in the Universe, and help derive the physics that can trace back to the creation of the universe. However, it is prohibitively slow for current sized datasets, and would continue to be a critical bottleneck with the trend of increasing dataset sizes to billions of particles and more, which makes TPCF a compelling benchmark application for future exa-scale architectures. State-of-the-art TPCF implementations do not map well to the underlying SIMD hardware, and also suffer from load-imbalance for large core counts. In this paper, we present a novel SIMD-friendly histogram update algorithm that exploits the spatial locality of histogram updates to achieve near-linear SIMD scaling. We also present a load-balancing scheme that combines domain-specific initial static division of work and dynamic task migration across nodes to effectively balance computation across nodes. Using Zin supercomputer at Lawrence Livermore National Laboratory (25,600 cores of Intel®Xeon®E5-2670, each with 256-bit SIMD), we achieve 90% parallel efficiency and 96% SIMD efficiency, and perform TPCF computation on a 1.7 billion particle dataset in 5.3 hours (at least 35× faster than previous approaches). In terms of cost per performance (measured in flops/$), we achieve at least an order-of-magnitude (11.1x) higher flops/$ as compared to the best known results [1]. Consequently, we now have line-of-sight to achieving the processing power for correlation computation to process billion+ particles telescopic data.

Inspired by the function, power, and volume of the organic brain, we are developing TrueNorth, a novel modular, non-von Neumann, ultra-low power, compact architecture. TrueNorth consists of a scalable network of neurosynaptic cores, with each core containing neurons, dendrites, synapses, and axons. To set sail for TrueNorth, we developed Compass, a multi-threaded, massively parallel functional simulator and a parallel compiler that maps a network of long-distance pathways in the macaque monkey brain to TrueNorth. We demonstrate near-perfect weak scaling on a 16 rack IBM® Blue Gene®/Q (262144 CPUs, 256 TB memory), achieving an unprecedented scale of 256 million neurosynaptic cores containing 65 billion neurons and 16 trillion synapses running only 388x slower than real time with an average spiking rate of 8.1 Hz. By using emerging PGAS communication primitives, we also demonstrate 2x better real-time performance over MPI primitives on a 4 rack Blue Gene/P (16384 CPUs, 16 TB memory).

The analysis of Cosmic Microwave Background (CMB) observations is a long-standing computational challenge, driven by the exponential growth in the size of the data sets being gathered. Since this growth is projected to continue for at least the next decade, it will be critical to extend the analysis algorithms and their implementations to peta-scale high performance computing (HPC) systems and beyond. The most computationally intensive part of the analysis is generating and reducing Monte Carlo realizations of an experiment’s data. In this work we take the current stateof-the-art simulation and mapping software and investigate its performance when pushed to tens of thousands of cores on a range of leading HPC systems, in particular focusing on the communication bottleneck that emerges at high concurrencies. We present a new communication strategy that removes this bottleneck, allowing for CMB analyses of unprecedented scale and hence fidelity. Experimental results show a communication speedup of up to 116 × using our alternative strategy. 1.

Summary form only given, as follows. The 25th year of IPDPS gives us the opportunity to look back and (to attempt) to assess what has gone wrong, what has gone well, and what came as a surprise, in the field of parallel and distributed processing. The panel members will give a few examples of striking events that took place in their area (covering Algorithms/ Applications/ Architectures/ Software). They will also give a short statement on how they would summarize the evolution of the field as a whole over the last 25 years.

The Thick-Restart Lanczos (TRLan) method is an effective method for solving large-scale Hermitian eigenvalue problems. The performance of the method strongly depends on the dimension of the projection subspace used at each restart. In this article, we propose an objective function to quantify the effectiveness of the selection of subspace dimension, and then introduce an adaptive scheme to dynamically select the dimension to optimize the performance. We have developed an open-source software package a --TRLan to include this adaptive scheme in the TRLan method. When applied to calculate the electronic structure of quantum dots, a --TRLan runs up to 2.3x faster than a state-of-the-art preconditioned conjugate gradient eigensolver.

In the quest for cognitive computing, we have built a massively parallel cortical simulator, C2, that incorporates a number of innovations in computation, memory, and communication. Using C2 on LLNL's Dawn Blue Gene/P supercomputer with 147, 456 CPUs and 144 TB of main memory, we report two cortical simulations -- at unprecedented scale -- that effectively saturate the entire memory capacity and refresh it at least every simulated second. The first simulation consists of 1.6 billion neurons and 8.87 trillion synapses with experimentally-measured gray matter thalamocortical connectivity. The second simulation has 900 million neurons and 9 trillion synapses with probabilistic connectivity. We demonstrate nearly perfect weak scaling and attractive strong scaling. The simulations, which incorporate phenomenological spiking neurons, individual learning synapses, axonal delays, and dynamic synaptic channels, exceed the scale of the cat cortex, marking the dawn of a new era in the scale of cortical simulations.

Green's function for the Laplace operator represents the propagation of influence of point sources and is the foundation for solving many physics problems. On a graph of pairwise similarities, the Green's function is the inverse of the combinatorial Laplacian; we resolve the zero-mode difficulty by showing its physical origin as the consequence of the Von Neumann boundary condition. We propose to use Green's function to propagate label information for both semi-supervised and unsupervised learning. We also derive this learning framework from the kernel regularization using Reproducing Kernel Hilbert Space theory at strong regularization limit. Green's function provides a well-defined distance metric on a generic weighted graph, either as the effective distance on the network of electric resistors, or the average commute time in random walks. We show that for unsupervised learning this approach is identical to Ratio Cut and Normalized Cut spectral clustering algorithms. Experiments on newsgroups and six UCI datasets illustrate the effectiveness of this approach. Finally, we propose a novel item-based recommender system using Green's function and show its effectiveness.

Two popular webpage ranking algorithms are HITS and PageRank. HITS emphasizes mutual reinforcement between authority and hub webpages, while PageRank emphasizes hyperlink weight normalization and web surfing based on random walk models. We systematically generalize/combine these concepts into a unified framework. The ranking framework contains a large algorithm space; HITS and PageRank are two extreme ends in this space. We study several normalized ranking algorithms which are intermediate between HITS and PageRank, and obtain closed-form solutions. We show that, to first order approximation, all ranking algorithms in this framework, including PageRank and HITS, lead to same ranking which is highly correlated with ranking by indegree.

It is well-known that for high dimensional data clustering, standard algorithms such as EM and K-means are often trapped in a local minimum. Many initialization methods have been proposed to tackle this problem, with only limited success. In this paper we propose a new approach to resolve this problem by repeated dimension reductions such that K-means or EM are performed only in very low dimensions. Cluster membership is utilized as a bridge between the reduced dimensional subspace and the original space, providing flexibility and ease of implementation. Clustering analysis performed on highly overlapped Gaussians, DNA gene expression profiles and Internet newsgroups demonstrate the effectiveness of the proposed algorithm.

Two popular link-based webpage ranking algorithms are (i) PageRank[1] and (ii) HITS (Hypertext Induced Topic Selection)[3]. HITS makes the crucial distinction of hubs and authorities and computes them in a mutually reinforcing way. PageRank considers the hyperlink weight normalization and the equilibrium distribution of random surfers as the citation score. We generalize and combine these key concepts into a unified framework, in which we prove that rankings produced by PageRank and HITS are both highly correlated with the ranking by in-degree and out-degree.

Many data types arising from data mining applications can be modeled as bipartite graphs, examples include terms and documents in a text corpus, customers and purchasing items in market basket analysis and reviewers and movies in a movie recommender system. In this paper, we propose a new data clustering method based on partitioning the underlying bipartite graph. The partition is constructed by minimizing a normalized sum of edge weights between unmatched pairs of vertices of the bipartite graph. We show that an approximate solution to the minimization problem can be obtained by computing a partial singular value decomposition (SVD) of the associated edge weight matrix of the bipartite graph. We point out the connection of our clustering algorithm to correspondence analysis used in multivariate analysis. We also briefly discuss the issue of assigning data objects to multiple clusters. In the experimental results, we apply our clustering algorithm to the problem of document clustering to illustrate its effectiveness and efficiency.

An important application of graph partitioning is data clustering using a graph model - the pairwise similarities between all data objects form a weighted graph adjacency matrix that contains all necessary information for clustering. In this paper, we propose a new algorithm for graph partitioning with an objective function that follows the min-max clustering principle. The relaxed version of the optimization of the min-max cut objective function leads to the Fiedler vector in spectral graph partitioning. Theoretical analyses of min-max cut indicate that it leads to balanced partitions, and lower bounds are derived. The min-max cut algorithm is tested on newsgroup data sets and is found to out-perform other current popular partitioning/clustering methods. The linkage-based refinements to the algorithm further improve the quality of clustering substantially. We also demonstrate that a linearized search order based on linkage differential is better than that based on the Fiedler vector, providing another effective partitioning method.

Grouping Web pages into distinct topics is one way of organizing the large amount of retrieved information on the Web. In this paper, we report that, based on a similarity metric, which incorporates textual information, hyperlink structure and co-citation relations, an unsupervised clustering method can automatically and effectively identify relevant topics, as shown in experiments on several retrieved sets of Web pages. The clustering method is a state-of-art spectral graph partitioning method based on the normalized cut criterion first developed for image segmentation.

The popular K-means clustering partitions a data set by minimiz(cid:173) ing a sum-of-squares cost function. A coordinate descend method is then used to find local minima. In this paper we show that the minimization can be reformulated as a trace maximization problem associated with the Gram matrix of the data vectors. Furthermore, we show that a relaxed version of the trace maximization problem possesses global optimal solutions which can be obtained by com(cid:173) puting a partial eigendecomposition of the Gram matrix, and the cluster assignment for each data vectors can be found by comput(cid:173) ing a pivoted QR decomposition of the eigenvector matrix. As a by-product we also derive a lower bound for the minimum of the sum-of-squares cost function.

Computational science problems with adaptive meshes involve dynamic load balancing when implemented on parallel machines. This dynamic load balancing requires fast partitioning of computational meshes at run time. We present in this report a scalable parallel dynamic partitioner, called S-HARP. The underlying principles of S-HARP are the fast feature of inertial partitioning and the quality feature of spectral partitioning. S-HARP is a universal dynamic partitioner with three distinctive features: (a) fast partitioning from scratch with a global view, requiring no information from the previous iterations, (b) no restriction on the issue of one partition per processor, (c) no imbalance factor issue because of precise bisection using sorting. Two types of parallelism have been exploited in S-HARP, fine-grain loop-level parallelism and coarse-grain recursive parallelism. The parallel partitioner has been implemented in Message Passing Interface on Cray T3E and IBM SP2 for portability. Experimental results indicate that S-HARP can partition a mesh of over 100,000 vertices into 256 partitions in 0.18 seconds on a 64-processor Cray T3E. S-HARP is much more scalable than other dynamic partitioners, giving over 17-fold speedup on 64 processors while ParaMeTiS1.0 gives a few-fold speedup. Experimental results demonstrate that S-HARP is three to 15 times faster than the other dynamic partitioners on computational meshes of size over 100,000 vertices while giving comparable edge cuts.

In the heart of most electronic structure simulation programs, there is a routine to find the solution of eigenvalue problems. Solving these eigenvalue problems usually dominates the computer time used for the whole simulation[6]. Because of their physical properties, these eigenvalue problems are always symmetric real or Hermitian. The dimensions of the matrices involved are usually very large and a large number of eigenvalues and their corresponding eigenvectors are needed to compute the desired physical quantities. To solve this type of problems, we introduce a variant of the Lanczos method called the thick-restart Lanczos method. In material science, this method is most appropriate for non-selfconsistent cases where the eigenvalue problems are linear and the number of required eigenvalues is relatively small compared to the size of the matrix.The Lanczos method is very simple and yet effective in finding eigenvalues. It is also well suited for parallel computing. There are two common ways of implementing the Lanczos method depending on whether the Lanczos vectors are stored. When the Lanczos vectors are not stored, they may lose orthogonality and the Lanczos method may generate spurious eigenvalues [2, 10]. Though spurious eigenvalues can be effectively identified, we still prefer not to deal with the spurious eigenvalues. When the Lanczos vectors are stored, the loss of orthogonality problem can be corrected by re-orthogonalization [4, 5, 7]. No spurious eigenvalue is generated in this case. However, because each Lanczos step generates one vector, a large amount of computer memory may be required to store all the Lanczos vectors. To limit the maximum amount of memory used, we typically restart the Lanczos algorithm after a certain number of steps. The restarted versions usually use considerably more matrix-vector multiplications than the non-restarted version. In recent years, newly developed restarting strategies have significantly reduced the number of matrix-vector multiplications used. The two most successful ones are the implicit restarting technique [1, 3, 8] and the dynamic thick-restart technique [9, 12]. For symmetric or Hermitian eigenvalue problems, these two schemes are equivalent. Because the thick-restart scheme is easier to implement and it is slightly more flexible than the implicit restarted scheme [9, 12], the new method described here uses the thick-restart scheme. Other thick-restart eigenvalue methods, e.g., the thick-restart Davidson method, can be applied on symmetric eigenvalue problems as well. Compared to them, the main advantage of the new scheme is that it uses less arithmetic operations by taking full advantage of the symmetry of the matrix [13].

Partitioningunstructured graphsis central to the parallel solution of computational science and engineering problems, Spectral partitioners, such recursive spectral bisection (RSB), have proven effective in generating high-quality partitions of realistically-sized meshes.The major problem which hindered their widespread use was their long execution times.This paper presents a new inertial spectral partitioned, called HARP.The main objective of the proposed approach is to quickly partition the meshes at runtime in a manner that works efficiently for real applications in the context of distributed-memory machines.The underlying principle of HARP is to find the eigenvectors of the unpartitioned vertices and then project them onto the eigenvectors of the originaJ mesh.Results for various meshes ranging in size from 1000 to 100,000 vertices indicate that HARP can indeed partition meshes rapidly at runtime, Experimental results show that our largest mesh can be partitioned sequentially in only a few seconds on an SP2 which is several times faster than other spectral partitioners while maintaining the solution quality of the proven RSB method.A parallel MPI version of HARP has also been implemented on IBM SP2 and Cray T3E.PrrralIel HARP, running on 64 processors SP2 and T3E, can partition a mesh containing more than 100,000 vertices into 64 subgrids in about half a second.These results indicate that graph partitioning can now be truly embedded in dynamically-changing real-world applications,

The computational requirements for an adaptive solution

On Paragon, two operating systems are available: OSF/1 AD and SUNMOS. The chief drawbacks of OSF/1 AD are: OSF/1 AD takes about 8 MB of memory on each node of the Paragon; messages can be sent only at a bandwidth of 30-35 MB per second compared to 200 MB per second peak advertised rate; latencies are on the order of 100 microseconds using Intel NX calls under OSF/1 AD. All these drawbacks can be minimized by using SUNMOS. SUNMOS takes only 250 KB of memory on each node and can send messages at bandwidth of 170 MB per second with latencies of 70 microseconds. We have measured the performance of applications under OSF/1 AD and SUNMOS and found that under OSF/1 AD, performance does not scale as the number of nodes increases, whereas under SUNMOS it seems to scale because of higher communication bandwidth.>

Abstract If problems involving unstructured meshes are to be solved efficiently on distributed‐memory parallel computers, the meshes must be partitioned and distributed across processors in a way that balances the computational load and minimizes communication. The recursive spectral bisection method (RSB) has been shown to be very effective for such partitioning problems compared to alternative methods, but RSB in its simplest form is expensive. Here a multilevel version of RSB is introduced that attains about an order‐of‐magnitude improvement in run time on typical examples.

A new algorithm for reducing the envelope of a sparse matrix is presented.This algorithm is based on the computation of eigenvectors of the Laplacian matrix associated with the graph of the sparse matrix.A reordering of the sparse matrix is determined based on the numerical values of the entries of an eigenvector of the Laplacian matrix.Numerical results show that the new reordering algorithm can in some cases reduce the envelope by more than a factor of two over the current standard algorithms such as Gibbs-Poole-Stockmeyer (GPS) or SPA RSPAK'S reverse Guthil!-McKee (RCM).Permission to copy witiout fce all or w of thts mmenal IS granted, provided tha! the copies am not made or disinbuted for dmct commercial advantaga, fhe ACM copy 'ight nofme and !he litlc of the pablicahon and 493 im dale appear, md notice is given Ibm copying is by pmnussion of lhe Association for Con,puung Maciinmy To cops ehenvise.or to republish.requwcs n fse mdhx specific permisaon

No abstract available.

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.>

The authors describe the novel spectral nested dissection (SND) algorithm, a novel algorithm for computing orderings appropriate for parallel factorization of sparse, symmetric matrices. The algorithm makes use of spectral properties of the Laplacian matrix associated with the given matrix to compute separators. The authors evaluate the quality of the spectral orderings with respect to several measures: fill, elimination tree height, height and weight balances of elimination trees, and clique tree heights. They use some very large structural analysis problems as test cases and demonstrate on these real applications that spectral orderings compare quite favorably with commonly used orderings, outperforming them by a wide margin for some of these measures. The only disadvantage of SND is its relatively long execution time.>

Article Free Access Share on The NAS parallel benchmarks—summary and preliminary results Authors: D. H. Bailey Numerical Aerodynamic Simulation (NAS) Systems Division, NASA Ames Research Center, Mail Stop T045-1, Moffett Field, CA Numerical Aerodynamic Simulation (NAS) Systems Division, NASA Ames Research Center, Mail Stop T045-1, Moffett Field, CAView Profile , E. Barszcz Numerical Aerodynamic Simulation (NAS) Systems Division, NASA Ames Research Center, Mail Stop T045-1, Moffett Field, CA Numerical Aerodynamic Simulation (NAS) Systems Division, NASA Ames Research Center, Mail Stop T045-1, Moffett Field, CAView Profile , J. T. Barton Numerical Aerodynamic Simulation (NAS) Systems Division, NASA Ames Research Center, Mail Stop T045-1, Moffett Field, CA Numerical Aerodynamic Simulation (NAS) Systems Division, NASA Ames Research Center, Mail Stop T045-1, Moffett Field, CAView Profile , D. S. Browning Numerical Aerodynamic Simulation (NAS) Systems Division, NASA Ames Research Center, Mail Stop T045-1, Moffett Field, CA Numerical Aerodynamic Simulation (NAS) Systems Division, NASA Ames Research Center, Mail Stop T045-1, Moffett Field, CAView Profile , R. L. Carter Numerical Aerodynamic Simulation (NAS) Systems Division, NASA Ames Research Center, Mail Stop T045-1, Moffett Field, CA Numerical Aerodynamic Simulation (NAS) Systems Division, NASA Ames Research Center, Mail Stop T045-1, Moffett Field, CAView Profile , L. Dagum Numerical Aerodynamic Simulation (NAS) Systems Division, NASA Ames Research Center, Mail Stop T045-1, Moffett Field, CA Numerical Aerodynamic Simulation (NAS) Systems Division, NASA Ames Research Center, Mail Stop T045-1, Moffett Field, CAView Profile , R. A. Fatoohi Numerical Aerodynamic Simulation (NAS) Systems Division, NASA Ames Research Center, Mail Stop T045-1, Moffett Field, CA Numerical Aerodynamic Simulation (NAS) Systems Division, NASA Ames Research Center, Mail Stop T045-1, Moffett Field, CAView Profile , P. O. Frederickson Numerical Aerodynamic Simulation (NAS) Systems Division, NASA Ames Research Center, Mail Stop T045-1, Moffett Field, CA Numerical Aerodynamic Simulation (NAS) Systems Division, NASA Ames Research Center, Mail Stop T045-1, Moffett Field, CAView Profile , T. A. Lasinski Numerical Aerodynamic Simulation (NAS) Systems Division, NASA Ames Research Center, Mail Stop T045-1, Moffett Field, CA Numerical Aerodynamic Simulation (NAS) Systems Division, NASA Ames Research Center, Mail Stop T045-1, Moffett Field, CAView Profile , R. S. Schreiber Numerical Aerodynamic Simulation (NAS) Systems Division, NASA Ames Research Center, Mail Stop T045-1, Moffett Field, CA Numerical Aerodynamic Simulation (NAS) Systems Division, NASA Ames Research Center, Mail Stop T045-1, Moffett Field, CAView Profile , H. D. Simon Numerical Aerodynamic Simulation (NAS) Systems Division, NASA Ames Research Center, Mail Stop T045-1, Moffett Field, CA Numerical Aerodynamic Simulation (NAS) Systems Division, NASA Ames Research Center, Mail Stop T045-1, Moffett Field, CAView Profile , V. Venkatakrishnan Numerical Aerodynamic Simulation (NAS) Systems Division, NASA Ames Research Center, Mail Stop T045-1, Moffett Field, CA Numerical Aerodynamic Simulation (NAS) Systems Division, NASA Ames Research Center, Mail Stop T045-1, Moffett Field, CAView Profile , S. K. Weeratunga Numerical Aerodynamic Simulation (NAS) Systems Division, NASA Ames Research Center, Mail Stop T045-1, Moffett Field, CA Numerical Aerodynamic Simulation (NAS) Systems Division, NASA Ames Research Center, Mail Stop T045-1, Moffett Field, CAView Profile Authors Info & Claims Supercomputing '91: Proceedings of the 1991 ACM/IEEE conference on SupercomputingAugust 1991 Pages 158–165https://doi.org/10.1145/125826.125925Published:01 August 1991Publication History 405citation1,162DownloadsMetricsTotal Citations405Total Downloads1,162Last 12 Months161Last 6 weeks25 Get Citation AlertsNew Citation Alert added!This alert has been successfully added and will be sent to:You will be notified whenever a record that you have chosen has been cited.To manage your alert preferences, click on the button below.Manage my AlertsNew Citation Alert!Please log in to your account Save to BinderSave to BinderCreate a New BinderNameCancelCreateExport CitationPublisher SiteeReaderPDF

The Gordon Bell Prize recognizes significant achievements in the application of supercomputers to scientific and engineering problems.In this special session the winners of the 1990 pm"ze will give presentations about i!heir winning entries in the competition.

This paper describes a new implementation of algorithms for solving large, dense symmetric eigen-problems AX = BX Λ, where the matrices A and B are too large to fit in the central memory of the computer. Here A is assumed to be symmetric, and B symmetric positive definite. A combination of block Cholesky and block Householder transformations are used to reduce the problem to a symmetric banded eigenproblem whose eigenvalues can be computed in central memory. Inverse iteration is applied to the banded matrix to compute selected eigenvectors, which are then transformed back to eigenvectors of the original problem. This method is especially suitable for the solution of large eigenproblems arising in quantum physics, using a vector supercomputer with fast secondary storage device such as the Cray X-MP with SSD. Some numerical results demonstrate the efficiency of the new implementation.