Download or read book Approximation with Kronecker Products written by Charles F. Van Loan and published by . This book was released on 1992 with total page 30 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book The Kronecker Product in Approximation and Fast Transform Generation written by Nikos Pitsianis and published by . This book was released on 1997 with total page 384 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Linear Algebra for Large Scale and Real Time Applications written by M.S. Moonen and published by Springer Science & Business Media. This book was released on 2013-11-09 with total page 434 pages. Available in PDF, EPUB and Kindle. Book excerpt: Proceedings of the NATO Advanced Study Institute, Leuven, Belgium, August 3-14, 1992

Download or read book Analyzing Markov Chains using Kronecker Products written by Tugrul Dayar and published by Springer Science & Business Media. This book was released on 2012-07-25 with total page 91 pages. Available in PDF, EPUB and Kindle. Book excerpt: Kronecker products are used to define the underlying Markov chain (MC) in various modeling formalisms, including compositional Markovian models, hierarchical Markovian models, and stochastic process algebras. The motivation behind using a Kronecker structured representation rather than a flat one is to alleviate the storage requirements associated with the MC. With this approach, systems that are an order of magnitude larger can be analyzed on the same platform. The developments in the solution of such MCs are reviewed from an algebraic point of view and possible areas for further research are indicated with an emphasis on preprocessing using reordering, grouping, and lumping and numerical analysis using block iterative, preconditioned projection, multilevel, decompositional, and matrix analytic methods. Case studies from closed queueing networks and stochastic chemical kinetics are provided to motivate decompositional and matrix analytic methods, respectively.

Download or read book A Matlab Object oriented Approach to Kronecker Product Approximation for Image Restoration written by Ryan R. Wright and published by . This book was released on 2002 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Matrix Computations written by Gene H. Golub and published by JHU Press. This book was released on 2013-02-15 with total page 781 pages. Available in PDF, EPUB and Kindle. Book excerpt: This revised edition provides the mathematical background and algorithmic skills required for the production of numerical software. It includes rewritten and clarified proofs and derivations, as well as new topics such as Arnoldi iteration, and domain decomposition methods.

Download or read book Combining Kronecker Product Approximation with Discrete Wavelet Transforms to Solve Dense Function related Linear Systems written by Judith M. Ford and published by . This book was released on 2003 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Tikhonov Regularization in Kronecker Product Approximation for Image Restoration with Mean Boundary Conditions written by and published by . This book was released on 2012 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Matrix Calculus And Kronecker Product A Practical Approach To Linear And Multilinear Algebra 2nd Edition written by Willi-hans Steeb and published by World Scientific Publishing Company. This book was released on 2011-03-24 with total page 323 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides a self-contained and accessible introduction to linear and multilinear algebra. Besides the standard techniques for linear and multilinear algebra many advanced topics are included. Emphasis is placed on the Kronecker product and tensor product. The Kronecker product has widespread applications in signal processing, discrete wavelets, statistical physics, computer graphics, fractals, quantum mechanics and quantum computing. All these fields are covered in detail. A key feature of the book is the many detailed worked-out examples. Computer algebra applications are also given. Each chapter includes useful exercises. The book is well suited for pure and applied mathematicians as well as theoretical physicists and engineers.New topics added to the second edition are: braid-like relations, Clebsch-Gordan expansion, nearest Kronecker product, Clifford and Pauli group, universal enveloping algebra, computer algebra and Kronecker product.

Download or read book Representation Discovery using Harmonic Analysis written by Sridhar López and published by Springer Nature. This book was released on 2022-05-31 with total page 147 pages. Available in PDF, EPUB and Kindle. Book excerpt: Representations are at the heart of artificial intelligence (AI). This book is devoted to the problem of representation discovery: how can an intelligent system construct representations from its experience? Representation discovery re-parameterizes the state space - prior to the application of information retrieval, machine learning, or optimization techniques - facilitating later inference processes by constructing new task-specific bases adapted to the state space geometry. This book presents a general approach to representation discovery using the framework of harmonic analysis, in particular Fourier and wavelet analysis. Biometric compression methods, the compact disc, the computerized axial tomography (CAT) scanner in medicine, JPEG compression, and spectral analysis of time-series data are among the many applications of classical Fourier and wavelet analysis. A central goal of this book is to show that these analytical tools can be generalized from their usual setting in (infinite-dimensional) Euclidean spaces to discrete (finite-dimensional) spaces typically studied in many subfields of AI. Generalizing harmonic analysis to discrete spaces poses many challenges: a discrete representation of the space must be adaptively acquired; basis functions are not pre-defined, but rather must be constructed. Algorithms for efficiently computing and representing bases require dealing with the curse of dimensionality. However, the benefits can outweigh the costs, since the extracted basis functions outperform parametric bases as they often reflect the irregular shape of a particular state space. Case studies from computer graphics, information retrieval, machine learning, and state space planning are used to illustrate the benefits of the proposed framework, and the challenges that remain to be addressed. Representation discovery is an actively developing field, and the author hopes this book will encourage other researchers to explore this exciting area of research. Table of Contents: Overview / Vector Spaces / Fourier Bases on Graphs / Multiscale Bases on Graphs / Scaling to Large Spaces / Case Study: State-Space Planning / Case Study: Computer Graphics / Case Study: Natural Language / Future Directions

Download or read book Kronecker Modeling and Analysis of Multidimensional Markovian Systems written by Tuğrul Dayar and published by Springer. This book was released on 2018-09-21 with total page 284 pages. Available in PDF, EPUB and Kindle. Book excerpt: This work considers Kronecker-based models with finite as well as countably infinite state spaces for multidimensional Markovian systems by paying particular attention to those whose reachable state spaces are smaller than their product state spaces. Numerical methods for steady-state and transient analysis of Kronecker-based multidimensional Markovian models are discussed in detail together with implementation issues. Case studies are provided to explain concepts and motivate use of methods. Having grown out of research from the past twenty years, this book expands upon the author’s previously published book Analyzing Markov Chains using Kronecker Products (Springer, 2012). The subject matter is interdisciplinary and at the intersection of applied mathematics and computer science. The book will be of use to researchers and graduate students with an understanding of basic linear algebra, probability, and discrete mathematics.

Download or read book Matrix Methods Theory Algorithms And Applications Dedicated To The Memory Of Gene Golub written by Vadim Olshevsky and published by World Scientific. This book was released on 2010-04-05 with total page 604 pages. Available in PDF, EPUB and Kindle. Book excerpt: Compared to other books devoted to matrices, this volume is unique in covering the whole of a triptych consisting of algebraic theory, algorithmic problems and numerical applications, all united by the essential use and urge for development of matrix methods. This was the spirit of the 2nd International Conference on Matrix Methods and Operator Equations from 23-27 July 2007 in Moscow that was organized by Dario Bini, Gene Golub, Alexander Guterman, Vadim Olshevsky, Stefano Serra-Capizzano, Gilbert Strang and Eugene Tyrtyshnikov.Matrix methods provide the key to many problems in pure and applied mathematics. However, linear algebra theory, numerical algorithms and matrices in FEM/BEM applications usually live as if in three separate worlds. In this volume, maybe for the first time ever, they are compiled together as one entity as it was at the Moscow meeting, where the algebraic part was impersonated by Hans Schneider, algorithms by Gene Golub, and applications by Guri Marchuk. All topics intervened in plenary sessions are specially categorized into three sections of this volume.The soul of the meeting was Gene Golub, who rendered a charming “Golub's dimension” to the three main axes of the conference topics. This volume is dedicated in gratitude to his memory.

Download or read book Interpolation and Least Squares Approximation in Bivariate Tensor Product Spaces written by Andrea Rott and published by Herbert Utz Verlag. This book was released on 1999 with total page 122 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Approximation Theory in Tensor Product Spaces written by William A. Light and published by Springer. This book was released on 2006-11-14 with total page 164 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Model Reduction and Approximation written by Peter Benner and published by SIAM. This book was released on 2017-07-06 with total page 421 pages. Available in PDF, EPUB and Kindle. Book excerpt: Many physical, chemical, biomedical, and technical processes can be described by partial differential equations or dynamical systems. In spite of increasing computational capacities, many problems are of such high complexity that they are solvable only with severe simplifications, and the design of efficient numerical schemes remains a central research challenge. This book presents a tutorial introduction to recent developments in mathematical methods for model reduction and approximation of complex systems. Model Reduction and Approximation: Theory and Algorithms contains three parts that cover (I) sampling-based methods, such as the reduced basis method and proper orthogonal decomposition, (II) approximation of high-dimensional problems by low-rank tensor techniques, and (III) system-theoretic methods, such as balanced truncation, interpolatory methods, and the Loewner framework. It is tutorial in nature, giving an accessible introduction to state-of-the-art model reduction and approximation methods. It also covers a wide range of methods drawn from typically distinct communities (sampling based, tensor based, system-theoretic).?? This book is intended for researchers interested in model reduction and approximation, particularly graduate students and young researchers.

Download or read book Latent Variable Analysis and Signal Separation written by Fabian Theis and published by Springer Science & Business Media. This book was released on 2012-03-01 with total page 552 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book constitutes the proceedings of the 10th International Conference on Latent Variable Analysis and Signal Separation, LVA/ICA 2012, held in Tel Aviv, Israel, in March 2012. The 20 revised full papers presented together with 42 revised poster papers, 1 keynote lecture, and 2 overview papers for the regular, as well as for the special session were carefully reviewed and selected from numerous submissions. Topics addressed are ranging from theoretical issues such as causality analysis and measures, through novel methods for employing the well-established concepts of sparsity and non-negativity for matrix and tensor factorization, down to a variety of related applications ranging from audio and biomedical signals to precipitation analysis.

Download or read book Solving Linear Systems Using Wavelet Compression Combined with Kronecker Product Approximation written by Judith M. Ford and published by . This book was released on 2003 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: