Fast Reliable Algorithms For Matrices With Structure
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Fast Reliable Algorithms For Matrices With Structure
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Author : T. Kailath
language : en
Publisher: SIAM
Release Date : 1999-01-01
Fast Reliable Algorithms For Matrices With Structure written by T. Kailath and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 1999-01-01 with Computers categories.
This book deals with the combined issues of speed and numerical reliability in algorithm development.
Fast Algorithms For Structured Matrices
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Author : Vadim Olshevsky
language : en
Publisher: American Mathematical Soc.
Release Date : 2003
Fast Algorithms For Structured Matrices written by Vadim Olshevsky and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003 with Mathematics categories.
One of the best known fast computational algorithms is the fast Fourier transform method. Its efficiency is based mainly on the special structure of the discrete Fourier transform matrix. Recently, many other algorithms of this type were discovered, and the theory of structured matrices emerged. This volume contains 22 survey and research papers devoted to a variety of theoretical and practical aspects of the design of fast algorithms for structured matrices and related issues. Included are several papers containing various affirmative and negative results in this direction. The theory of rational interpolation is one of the excellent sources providing intuition and methods to design fast algorithms. The volume contains several computational and theoretical papers on the topic. There are several papers on new applications of structured matrices, e.g., to the design of fast decoding algorithms, computing state-space realizations, relations to Lie algebras, unconstrained optimization, solving matrix equations, etc. The book is suitable for mathematicians, engineers, and numerical analysts who design, study, and use fast computational algorithms based on the theory of structured matrices.
Structured Matrices In Mathematics Computer Science And Engineering Ii
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Author : Vadim Olshevsky
language : en
Publisher: American Mathematical Soc.
Release Date : 2001
Structured Matrices In Mathematics Computer Science And Engineering Ii written by Vadim Olshevsky and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2001 with Mathematics categories.
"The collection of the contributions to these volumes offers a flavor of the plethora of different approaches to attack structured matrix problems. The reader will find that the theory of structured matrices is positioned to bridge diverse applications in the sciences and engineering, deep mathematical theories, as well as computational and numberical issues. The presentation fully illustrates the fact that the technicques of engineers, mathematicisn, and numerical analysts nicely complement each other, and they all contribute to one unified theory of structured matrices"--Back cover.
Templates For The Solution Of Algebraic Eigenvalue Problems
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Author : Zhaojun Bai
language : en
Publisher: SIAM
Release Date : 2000-01-01
Templates For The Solution Of Algebraic Eigenvalue Problems written by Zhaojun Bai and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 2000-01-01 with Computers categories.
Large-scale problems of engineering and scientific computing often require solutions of eigenvalue and related problems. This book gives a unified overview of theory, algorithms, and practical software for eigenvalue problems. It organizes this large body of material to make it accessible for the first time to the many nonexpert users who need to choose the best state-of-the-art algorithms and software for their problems. Using an informal decision tree, just enough theory is introduced to identify the relevant mathematical structure that determines the best algorithm for each problem.
Dynamics Of Civil Structures Volume 2
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Author : Juan Caicedo
language : en
Publisher: Springer
Release Date : 2017-06-01
Dynamics Of Civil Structures Volume 2 written by Juan Caicedo and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-06-01 with Technology & Engineering categories.
Dynamics of Civil Structures, Volume 2: Proceedings of the 35th IMAC, A Conference and Exposition on Structural Dynamics, 2017, the second volume of ten from the Conference brings together contributions to this important area of research and engineering. The collection presents early findings and case studies on fundamental and applied aspects of the Dynamics of Civil Structures, including papers on: Modal Parameter Identification Dynamic Testing of Civil Structures Control of Human Induced Vibrations of Civil Structures Model Updating Damage Identification in Civil Infrastructure Bridge Dynamics Experimental Techniques for Civil Structures Hybrid Simulation of Civil Structures Vibration Control of Civil Structures System Identification of Civil Structures
Tensor Numerical Methods In Scientific Computing
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Author : Boris N. Khoromskij
language : en
Publisher: Walter de Gruyter GmbH & Co KG
Release Date : 2018-06-11
Tensor Numerical Methods In Scientific Computing written by Boris N. Khoromskij and has been published by Walter de Gruyter GmbH & Co KG this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-06-11 with Mathematics categories.
The most difficult computational problems nowadays are those of higher dimensions. This research monograph offers an introduction to tensor numerical methods designed for the solution of the multidimensional problems in scientific computing. These methods are based on the rank-structured approximation of multivariate functions and operators by using the appropriate tensor formats. The old and new rank-structured tensor formats are investigated. We discuss in detail the novel quantized tensor approximation method (QTT) which provides function-operator calculus in higher dimensions in logarithmic complexity rendering super-fast convolution, FFT and wavelet transforms. This book suggests the constructive recipes and computational schemes for a number of real life problems described by the multidimensional partial differential equations. We present the theory and algorithms for the sinc-based separable approximation of the analytic radial basis functions including Green’s and Helmholtz kernels. The efficient tensor-based techniques for computational problems in electronic structure calculations and for the grid-based evaluation of long-range interaction potentials in multi-particle systems are considered. We also discuss the QTT numerical approach in many-particle dynamics, tensor techniques for stochastic/parametric PDEs as well as for the solution and homogenization of the elliptic equations with highly-oscillating coefficients. Contents Theory on separable approximation of multivariate functions Multilinear algebra and nonlinear tensor approximation Superfast computations via quantized tensor approximation Tensor approach to multidimensional integrodifferential equations
Mathematics In Signal Processing V
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Author : J. G. McWhirter
language : en
Publisher: Oxford University Press
Release Date : 2002
Mathematics In Signal Processing V written by J. G. McWhirter and has been published by Oxford University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2002 with Computers categories.
This is a collection of papers from the IMA conference on Mathematics in Signal Processing. Signal processing is an important industrial area for the application of mathematical concepts - it has recently been fuelled by developments in mobile communications, multimedia systems and digital TV. This collection of papers presents a good coverage of current activity on this subject worldwide and is of interest to those in industry carrying out research into signal processing for communications, sonar, radar, navigation and biomedical applications, and to academic mathematicians identifying new mathematical problems.
Structured Matrices And Polynomials
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Author : Victor Y. Pan
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Structured Matrices And Polynomials written by Victor Y. Pan and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
Structured matrices serve as a natural bridge between the areas of algebraic computations with polynomials and numerical matrix computations, allowing cross-fertilization of both fields. This book covers most fundamental numerical and algebraic computations with Toeplitz, Hankel, Vandermonde, Cauchy, and other popular structured matrices. Throughout the computations, the matrices are represented by their compressed images, called displacements, enabling both a unified treatment of various matrix structures and dramatic saving of computer time and memory. The resulting superfast algorithms allow further dramatic parallel acceleration using FFT and fast sine and cosine transforms. Included are specific applications to other fields, in particular, superfast solutions to: various fundamental problems of computer algebra; the tangential Nevanlinna--Pick and matrix Nehari problems The primary intended readership for this work includes researchers, algorithm designers, and advanced graduate students in the fields of computations with structured matrices, computer algebra, and numerical rational interpolation. The book goes beyond research frontiers and, apart from very recent research articles, includes yet unpublished results. To serve a wider audience, the presentation unfolds systematically and is written in a user-friendly engaging style. Only some preliminary knowledge of the fundamentals of linear algebra is required. This makes the material accessible to graduate students and new researchers who wish to study the rapidly exploding area of computations with structured matrices and polynomials. Examples, tables, figures, exercises, extensive bibliography, and index lend this text to classroom use or self-study.
Matrix Computations And Semiseparable Matrices
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Author : Raf Vandebril
language : en
Publisher: JHU Press
Release Date : 2008-01-14
Matrix Computations And Semiseparable Matrices written by Raf Vandebril and has been published by JHU Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008-01-14 with Mathematics categories.
In recent years several new classes of matrices have been discovered and their structure exploited to design fast and accurate algorithms. In this new reference work, Raf Vandebril, Marc Van Barel, and Nicola Mastronardi present the first comprehensive overview of the mathematical and numerical properties of the family's newest member: semiseparable matrices. The text is divided into three parts. The first provides some historical background and introduces concepts and definitions concerning structured rank matrices. The second offers some traditional methods for solving systems of equations involving the basic subclasses of these matrices. The third section discusses structured rank matrices in a broader context, presents algorithms for solving higher-order structured rank matrices, and examines hybrid variants such as block quasiseparable matrices. An accessible case study clearly demonstrates the general topic of each new concept discussed. Many of the routines featured are implemented in Matlab and can be downloaded from the Web for further exploration.
Numerical Methods For Structured Markov Chains
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Author : Dario A. Bini
language : en
Publisher: OUP Oxford
Release Date : 2005-02-03
Numerical Methods For Structured Markov Chains written by Dario A. Bini and has been published by OUP Oxford this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005-02-03 with Mathematics categories.
Intersecting two large research areas - numerical analysis and applied probability/queuing theory - this book is a self-contained introduction to the numerical solution of structured Markov chains, which have a wide applicability in queuing theory and stochastic modeling and include M/G/1 and GI/M/1-type Markov chain, quasi-birth-death processes, non-skip free queues and tree-like stochastic processes. Written for applied probabilists and numerical analysts, but accessible to engineers and scientists working on telecommunications and evaluation of computer systems performances, it provides a systematic treatment of the theory and algorithms for important families of structured Markov chains and a thorough overview of the current literature. The book, consisting of nine Chapters, is presented in three parts. Part 1 covers a basic description of the fundamental concepts related to Markov chains, a systematic treatment of the structure matrix tools, including finite Toeplitz matrices, displacement operators, FFT, and the infinite block Toeplitz matrices, their relationship with matrix power series and the fundamental problems of solving matrix equations and computing canonical factorizations. Part 2 deals with the description and analysis of structure Markov chains and includes M/G/1, quasi-birth-death processes, non-skip-free queues and tree-like processes. Part 3 covers solution algorithms where new convergence and applicability results are proved. Each chapter ends with bibliographic notes for further reading, and the book ends with an appendix collecting the main general concepts and results used in the book, a list of the main annotations and algorithms used in the book, and an extensive index.