Download or read book Algorithms for Large Scale Problems in Eigenvalue and SVD Computations and in Big Data Applications written by Lingfei Wu and published by . This book was released on 2016 with total page 131 pages. Available in PDF, EPUB and Kindle. Book excerpt: As big data has increasing influence on our daily life and research activities, it poses significant challenges on various research areas. Some applications often demand a fast solution of large, sparse eigenvalue and singular value problems; In other applications, extracting knowledge from large-scale data requires many techniques such as statistical calculations, data mining, and high performance computing. In this dissertation, we develop efficient and robust iterative methods and software for the computation of eigenvalue and singular values. We also develop practical numerical and data mining techniques to estimate the trace of a function of a large, sparse matrix and to detect in real-time blob-filaments in fusion plasma on extremely large parallel computers. In the first work, we propose a hybrid two stage SVD method for efficiently and accurately computing a few extreme singular triplets, especially the ones corresponding to the smallest singular values. The first stage achieves fast convergence while the second achieves the final accuracy. Furthermore, we develop a high-performance preconditioned SVD software based on the proposed method on top of the state-of-the-art eigensolver PRIMME. The method can be used with or without preconditioning, on parallel computers, and is superior to other state-of-the-art SVD methods in both efficiency and robustness. In the second study, we provide insights and develop practical algorithms to accomplish efficient and accurate computation of interior eigenpairs using refined projection techniques in non-Krylov iterative methods. By analyzing different implementations of the refined projection, we propose a new hybrid method to efficiently find interior eigenpairs without compromising accuracy. Our numerical experiments illustrate the efficiency and robustness of the proposed method. In the third work, we present a novel method to estimate the trace of matrix inverse that exploits the pattern correlation between the diagonal of the inverse of the matrix and that of some approximate inverse. We leverage various sampling and fitting techniques to fit the diagonal of the approximation to that of the inverse. Our method may serve as a standalone kernel for providing a fast trace estimate or as a variance reduction method for Monte Carlo in some cases. An extensive set of experiments demonstrate the potential of our method. In the fourth study, we provide first results on applying outlier detection techniques to effectively tackle the fusion blob detection problem on extremely large parallel machines. We present a real-time region outlier detection algorithm to efficiently find and track blobs in fusion experiments and simulations. Our experiments demonstrated we can achieve linear time speedup up to 1024 MPI processes and complete blob detection in two or three milliseconds.

Download or read book Large Scale Eigenvalue Problems written by J. Cullum and published by Elsevier. This book was released on 1986-01-01 with total page 339 pages. Available in PDF, EPUB and Kindle. Book excerpt: Results of research into large scale eigenvalue problems are presented in this volume. The papers fall into four principal categories:novel algorithms for solving large eigenvalue problems, novel computer architectures, computationally-relevant theoretical analyses, and problems where large scale eigenelement computations have provided new insight.

Download or read book Eigenvalue Problems Algorithms Software and Applications in Petascale Computing written by Tetsuya Sakurai and published by Springer. This book was released on 2018-01-03 with total page 312 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides state-of-the-art and interdisciplinary topics on solving matrix eigenvalue problems, particularly by using recent petascale and upcoming post-petascale supercomputers. It gathers selected topics presented at the International Workshops on Eigenvalue Problems: Algorithms; Software and Applications, in Petascale Computing (EPASA2014 and EPASA2015), which brought together leading researchers working on the numerical solution of matrix eigenvalue problems to discuss and exchange ideas – and in so doing helped to create a community for researchers in eigenvalue problems. The topics presented in the book, including novel numerical algorithms, high-performance implementation techniques, software developments and sample applications, will contribute to various fields that involve solving large-scale eigenvalue problems.

Download or read book Numerical Methods for Large Eigenvalue Problems written by Yousef Saad and published by SIAM. This book was released on 2011-01-01 with total page 292 pages. Available in PDF, EPUB and Kindle. Book excerpt: This revised edition discusses numerical methods for computing eigenvalues and eigenvectors of large sparse matrices. It provides an in-depth view of the numerical methods that are applicable for solving matrix eigenvalue problems that arise in various engineering and scientific applications. Each chapter was updated by shortening or deleting outdated topics, adding topics of more recent interest, and adapting the Notes and References section. Significant changes have been made to Chapters 6 through 8, which describe algorithms and their implementations and now include topics such as the implicit restart techniques, the Jacobi-Davidson method, and automatic multilevel substructuring.

Download or read book Lanczos Algorithms for Large Symmetric Eigenvalue Computations written by Jane K. Cullum and published by SIAM. This book was released on 2002-09-01 with total page 290 pages. Available in PDF, EPUB and Kindle. Book excerpt: First published in 1985, this book presents background material, descriptions, and supporting theory relating to practical numerical algorithms for the solution of huge eigenvalue problems. This book deals with 'symmetric' problems. However, in this book, 'symmetric' also encompasses numerical procedures for computing singular values and vectors of real rectangular matrices and numerical procedures for computing eigenelements of nondefective complex symmetric matrices. Although preserving orthogonality has been the golden rule in linear algebra, most of the algorithms in this book conform to that rule only locally, resulting in markedly reduced memory requirements. Additionally, most of the algorithms discussed separate the eigenvalue (singular value) computations from the corresponding eigenvector (singular vector) computations. This separation prevents losses in accuracy that can occur in methods which, in order to be able to compute further into the spectrum, use successive implicit deflation by computed eigenvector or singular vector approximations.

Download or read book Inverse Eigenvalue Problems written by Moody Chu and published by Oxford University Press. This book was released on 2005-06-16 with total page 408 pages. Available in PDF, EPUB and Kindle. Book excerpt: Inverse eigenvalue problems arise in a remarkable variety of applications and associated with any inverse eigenvalue problem are two fundamental questions--the theoretical issue of solvability and the practical issue of computability. Both questions are difficult and challenging. In this text, the authors discuss the fundamental questions, some known results, many applications, mathematical properties, a variety of numerical techniques, as well as several open problems.This is the first book in the authoritative Numerical Mathematics and Scientific Computation series to cover numerical linear algebra, a broad area of numerical analysis. Authored by two world-renowned researchers, the book is aimed at graduates and researchers in applied mathematics, engineering and computer science and makes an ideal graduate text.

Download or read book Lanczos Algorithms for Large Symmetric Eigenvalue Computations Vol I Theory written by CULLUM and published by Birkhäuser. This book was released on 2012-05-06 with total page 273 pages. Available in PDF, EPUB and Kindle. Book excerpt: Energy levels, resonanees, vibrations, feature extraetion, faetor analysis - the names vary from discipline to diseipline; however, all involve eigenvalue/eigenveetor eomputations. An engineer or physicist who is modeling a physieal proeess, strueture, or deviee is eonstrained to seleet a model for whieh the subsequently-required eomputations ean be performed. This eonstraint often leads to redueed order or redueed size models whieh may or may not preserve all of the important eharaeteristies of the system being modeled. Ideally, the modeler should not be foreed to make such apriori reduetions. It is our intention to provide here proeedures wh ich will allow the direct and suceessful solution of many large 'symmetrie' eigenvalue problems, so that at least in problems where the computations are of this type there will be no need for model reduetion. Matrix eigenelement eomputations can be c1assified as smalI, medium, or large seale, in terms of their relative degrees of difficulty as measured by the amount of computer storage and time required to eomplete the desired eomputations. A matrix eigenvalue problem is said to be sm all scale if the given matrix has order smaller than 100. Well-documented and reliable FORTRAN pro grams exist for small scale eigenelement computations, see in particular ElS­ PACK [1976,1977]. Typically those programs explicitly trans form the given matrix into a simpler canonieal form. The eigenelement eomputations are then performed on the canonical form.

Download or read book Handbook of Big Data written by Peter Bühlmann and published by CRC Press. This book was released on 2016-02-22 with total page 480 pages. Available in PDF, EPUB and Kindle. Book excerpt: Handbook of Big Data provides a state-of-the-art overview of the analysis of large-scale datasets. Featuring contributions from well-known experts in statistics and computer science, this handbook presents a carefully curated collection of techniques from both industry and academia. Thus, the text instills a working understanding of key statistical

Download or read book Frontiers in Massive Data Analysis written by National Research Council and published by National Academies Press. This book was released on 2013-09-03 with total page 191 pages. Available in PDF, EPUB and Kindle. Book excerpt: Data mining of massive data sets is transforming the way we think about crisis response, marketing, entertainment, cybersecurity and national intelligence. Collections of documents, images, videos, and networks are being thought of not merely as bit strings to be stored, indexed, and retrieved, but as potential sources of discovery and knowledge, requiring sophisticated analysis techniques that go far beyond classical indexing and keyword counting, aiming to find relational and semantic interpretations of the phenomena underlying the data. Frontiers in Massive Data Analysis examines the frontier of analyzing massive amounts of data, whether in a static database or streaming through a system. Data at that scale-terabytes and petabytes-is increasingly common in science (e.g., particle physics, remote sensing, genomics), Internet commerce, business analytics, national security, communications, and elsewhere. The tools that work to infer knowledge from data at smaller scales do not necessarily work, or work well, at such massive scale. New tools, skills, and approaches are necessary, and this report identifies many of them, plus promising research directions to explore. Frontiers in Massive Data Analysis discusses pitfalls in trying to infer knowledge from massive data, and it characterizes seven major classes of computation that are common in the analysis of massive data. Overall, this report illustrates the cross-disciplinary knowledge-from computer science, statistics, machine learning, and application disciplines-that must be brought to bear to make useful inferences from massive data.

Download or read book The Dictionary of Artificial Intelligence written by Utku Taşova and published by Entropol. This book was released on 2023-11-03 with total page 565 pages. Available in PDF, EPUB and Kindle. Book excerpt: Unveiling the Future: Your Portal to Artificial Intelligence Proficiency In the epoch of digital metamorphosis, Artificial Intelligence (AI) stands as the vanguard of a new dawn, a nexus where human ingenuity intertwines with machine precision. As we delve deeper into this uncharted realm, the boundary between the conceivable and the fantastical continually blurs, heralding a new era of endless possibilities. The Dictionary of Artificial Intelligence, embracing a compendium of 3,300 meticulously curated titles, endeavors to be the torchbearer in this journey of discovery, offering a wellspring of knowledge to both the uninitiated and the adept. Embarking on the pages of this dictionary is akin to embarking on a voyage through the vast and often turbulent seas of AI. Each entry serves as a beacon, illuminating complex terminologies, core principles, and the avant-garde advancements that characterize this dynamic domain. The dictionary is more than a mere compilation of terms; it's a labyrinth of understanding waiting to be traversed. The Dictionary of Artificial Intelligence is an endeavor to demystify the arcane, to foster a shared lexicon that enhances collaboration, innovation, and comprehension across the AI community. It's a mission to bridge the chasm between ignorance and insight, to unravel the intricacies of AI that often seem enigmatic to the outsiders. This profound reference material transcends being a passive repository of terms; it’s an engagement with the multifaceted domain of artificial intelligence. Each title encapsulated within these pages is a testament to the audacity of human curiosity and the unyielding quest for advancement that propels the AI domain forward. The Dictionary of Artificial Intelligence is an invitation to delve deeper, to grapple with the lexicon of a field that stands at the cusp of redefining the very fabric of society. It's a conduit through which the curious become enlightened, the proficient become masters, and the innovators find inspiration. As you traverse through the entries of The Dictionary of Artificial Intelligence, you are embarking on a journey of discovery. A journey that not only augments your understanding but also ignites the spark of curiosity and the drive for innovation that are quintessential in navigating the realms of AI. We beckon you to commence this educational expedition, to explore the breadth and depth of AI lexicon, and to emerge with a boundless understanding and an unyielding resolve to contribute to the ever-evolving narrative of artificial intelligence. Through The Dictionary of Artificial Intelligence, may your quest for knowledge be as boundless and exhilarating as the domain it explores.

Download or read book Advances in Neural Networks ISNN 2014 written by Zhigang Zeng and published by Springer. This book was released on 2014-11-28 with total page 661 pages. Available in PDF, EPUB and Kindle. Book excerpt: The volume LNCS 8866 constitutes the refereed proceedings of the 11th International Symposium on Neural Networks, ISNN 2014, held in Hong Kong and Macao, China on November/ December 2014. The 71 revised full papers presented were carefully reviewed and selected from 119 submissions. These papers cover all major topics of the theoretical research, empirical study and applications of neural networks research as follows. The focus is on following topics such as analysis, modeling, and applications.

Download or read book Modern Algorithms for Large Sparse Eigenvalue Problems written by Arnd Meyer and published by Walter de Gruyter GmbH & Co KG. This book was released on 1987-12-31 with total page 132 pages. Available in PDF, EPUB and Kindle. Book excerpt: No detailed description available for "Modern Algorithms for Large Sparse Eigenvalue Problems".

Download or read book Lanczos Algorithms for Large Symmetric Eigenvalue Computations Vol II Programs written by Cullum and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 508 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Theory and Computation of Complex Tensors and its Applications written by Maolin Che and published by Springer Nature. This book was released on 2020-04-01 with total page 250 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book provides an introduction of very recent results about the tensors and mainly focuses on the authors' work and perspective. A systematic description about how to extend the numerical linear algebra to the numerical multi-linear algebra is also delivered in this book. The authors design the neural network model for the computation of the rank-one approximation of real tensors, a normalization algorithm to convert some nonnegative tensors to plane stochastic tensors and a probabilistic algorithm for locating a positive diagonal in a nonnegative tensors, adaptive randomized algorithms for computing the approximate tensor decompositions, and the QR type method for computing U-eigenpairs of complex tensors. This book could be used for the Graduate course, such as Introduction to Tensor. Researchers may also find it helpful as a reference in tensor research.

Download or read book Numerical Algorithms written by Justin Solomon and published by CRC Press. This book was released on 2015-06-24 with total page 400 pages. Available in PDF, EPUB and Kindle. Book excerpt: Numerical Algorithms: Methods for Computer Vision, Machine Learning, and Graphics presents a new approach to numerical analysis for modern computer scientists. Using examples from a broad base of computational tasks, including data processing, computational photography, and animation, the textbook introduces numerical modeling and algorithmic desig

Download or read book Graph Based Social Media Analysis written by Ioannis Pitas and published by CRC Press. This book was released on 2016-04-19 with total page 436 pages. Available in PDF, EPUB and Kindle. Book excerpt: Focused on the mathematical foundations of social media analysis, Graph-Based Social Media Analysis provides a comprehensive introduction to the use of graph analysis in the study of social and digital media. It addresses an important scientific and technological challenge, namely the confluence of graph analysis and network theory with linear alge

Download or read book Using Parallel Banded Linear System Solvers in Generalized Eigenvalue Problems written by Hong Zhang and published by . This book was released on 1993 with total page 24 pages. Available in PDF, EPUB and Kindle. Book excerpt: Abstract: "Subspace iteration is a reliable and cost effective method for solving positive definite banded symmetric generalized eigenproblems, especially in the case of large scale problems. This paper discusses an algorithm that makes use of two parallel banded solvers in subspace iteration. A shift is introduced to decompose the banded linear systems into relatively independent subsystems and to accelerate the iterations. With this shift, an eigenproblem is mapped efficiently into the memories of a multiprocessor and a high speed-up is obtained for parallel implementations. An optimal shift is a shift that balances total computation and communication costs. Under certain conditions, we show how to estimate an optimal shift analytically using the decay rate for the inverse of a banded matrix, and how to improve this estimate. Computational results on iPSC/2 and iPSC/860 multiprocessors are presented."