Guaranteed Accuracy In Numerical Linear Algebra

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Guaranteed Accuracy in Numerical Linear Algebra

Author : S.K. Godunov
Publisher : Springer Science & Business Media
ISBN 13 : 940111952X
Total Pages : 545 pages
Book Rating : 4.4/5 (11 download)

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Book Synopsis Guaranteed Accuracy in Numerical Linear Algebra by : S.K. Godunov

Download or read book Guaranteed Accuracy in Numerical Linear Algebra written by S.K. Godunov and published by Springer Science & Business Media. This book was released on 2013-03-14 with total page 545 pages. Available in PDF, EPUB and Kindle. Book excerpt: There exists a vast literature on numerical methods of linear algebra. In our bibliography list, which is by far not complete, we included some monographs on the subject [46], [15], [32], [39], [11], [21]. The present book is devoted to the theory of algorithms for a single problem of linear algebra, namely, for the problem of solving systems of linear equations with non-full-rank matrix of coefficients. The solution of this problem splits into many steps, the detailed discussion of which are interest ing problems on their own (bidiagonalization of matrices, computation of singular values and eigenvalues, procedures of deflation of singular values, etc. ). Moreover, the theory of algorithms for solutions of the symmetric eigenvalues problem is closely related to the theory of solv ing linear systems (Householder's algorithms of bidiagonalization and tridiagonalization, eigenvalues and singular values, etc. ). It should be stressed that in this book we discuss algorithms which to computer programs having the virtue that the accuracy of com lead putations is guaranteed. As far as the final program product is con cerned, this means that the user always finds an unambiguous solution of his problem. This solution might be of two kinds: 1. Solution of the problem with an estimate of errors, where abso lutely all errors of input data and machine round-offs are taken into account. 2.

Numerical Linear Algebra and Applications

Author : Biswa Nath Datta
Publisher : SIAM
ISBN 13 : 0898717655
Total Pages : 546 pages
Book Rating : 4.8/5 (987 download)

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Book Synopsis Numerical Linear Algebra and Applications by : Biswa Nath Datta

Download or read book Numerical Linear Algebra and Applications written by Biswa Nath Datta and published by SIAM. This book was released on 2010-01-01 with total page 546 pages. Available in PDF, EPUB and Kindle. Book excerpt: Full of features and applications, this acclaimed textbook for upper undergraduate level and graduate level students includes all the major topics of computational linear algebra, including solution of a system of linear equations, least-squares solutions of linear systems, computation of eigenvalues, eigenvectors, and singular value problems. Drawing from numerous disciplines of science and engineering, the author covers a variety of motivating applications. When a physical problem is posed, the scientific and engineering significance of the solution is clearly stated. Each chapter contains a summary of the important concepts developed in that chapter, suggestions for further reading, and numerous exercises, both theoretical and MATLAB and MATCOM based. The author also provides a list of key words for quick reference. The MATLAB toolkit available online, 'MATCOM', contains implementations of the major algorithms in the book and will enable students to study different algorithms for the same problem, comparing efficiency, stability, and accuracy.

Lectures on Finite Precision Computations

Author : Francoise Chaitin-Chatelin
Publisher : SIAM
ISBN 13 : 0898713587
Total Pages : 244 pages
Book Rating : 4.8/5 (987 download)

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Book Synopsis Lectures on Finite Precision Computations by : Francoise Chaitin-Chatelin

Download or read book Lectures on Finite Precision Computations written by Francoise Chaitin-Chatelin and published by SIAM. This book was released on 1996-01-01 with total page 244 pages. Available in PDF, EPUB and Kindle. Book excerpt: Mathematics of Computing -- Numerical Analysis.

Numerical Linear Algebra

Author : V. SUNDARAPANDIAN
Publisher : PHI Learning Pvt. Ltd.
ISBN 13 : 8120334361
Total Pages : 616 pages
Book Rating : 4.1/5 (23 download)

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Book Synopsis Numerical Linear Algebra by : V. SUNDARAPANDIAN

Download or read book Numerical Linear Algebra written by V. SUNDARAPANDIAN and published by PHI Learning Pvt. Ltd.. This book was released on 2008-04-23 with total page 616 pages. Available in PDF, EPUB and Kindle. Book excerpt: This well-organized text provides a clear analysis of the fundamental concepts of numerical linear algebra. It presents various numerical methods for the basic topics of linear algebra with a detailed discussion on theory, algorithms, and MATLAB implementation. The book provides a review of matrix algebra and its important results in the opening chapter and examines these results in the subsequent chapters. With clear explanations, the book analyzes different kinds of numerical algorithms for solving linear algebra such as the elimination and iterative methods for linear systems, the condition number of a matrix, singular value decomposition (SVD) of a matrix, and linear least-squares problem. In addition, it describes the Householder and Givens matrices and their applications, and the basic numerical methods for solving the matrix eigenvalue problem. Finally, the text reviews the numerical methods for systems and control. Key Features Includes numerous worked-out examples to help students grasp the concepts easily.  Provides chapter-end exercises to enable students to check their comprehension of the topics discussed.  Gives answers to exercises with hints at the end of the book.  Uses MATLAB software for problem-solving. Primarily designed as a textbook for postgraduate students of Mathematics, this book would also serve as a handbook on matrix computations for scientists and engineers.

Error Control and Adaptivity in Scientific Computing

Author : Haydar Bulgak
Publisher : Springer Science & Business Media
ISBN 13 : 9401146470
Total Pages : 364 pages
Book Rating : 4.4/5 (11 download)

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Book Synopsis Error Control and Adaptivity in Scientific Computing by : Haydar Bulgak

Download or read book Error Control and Adaptivity in Scientific Computing written by Haydar Bulgak and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 364 pages. Available in PDF, EPUB and Kindle. Book excerpt: One of the main ways by which we can understand complex processes is to create computerised numerical simulation models of them. Modern simulation tools are not used only by experts, however, and reliability has therefore become an important issue, meaning that it is not sufficient for a simulation package merely to print out some numbers, claiming them to be the desired results. An estimate of the associated error is also needed. The errors may derive from many sources: errors in the model, errors in discretization, rounding errors, etc. Unfortunately, this situation does not obtain for current packages and there is a great deal of room for improvement. Only if the error can be estimated is it possible to do something to reduce it. The contributions in this book cover many aspects of the subject, the main topics being error estimates and error control in numerical linear algebra algorithms (closely related to the concept of condition numbers), interval arithmetic and adaptivity for continuous models.

Spectra and Pseudospectra

Author : Lloyd N. Trefethen
Publisher : Princeton University Press
ISBN 13 : 9780691119465
Total Pages : 634 pages
Book Rating : 4.1/5 (194 download)

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Book Synopsis Spectra and Pseudospectra by : Lloyd N. Trefethen

Download or read book Spectra and Pseudospectra written by Lloyd N. Trefethen and published by Princeton University Press. This book was released on 2005-08-07 with total page 634 pages. Available in PDF, EPUB and Kindle. Book excerpt: Pure and applied mathematicians, physicists, scientists, and engineers use matrices and operators and their eigenvalues in quantum mechanics, fluid mechanics, structural analysis, acoustics, ecology, numerical analysis, and many other areas. However, in some applications the usual analysis based on eigenvalues fails. For example, eigenvalues are often ineffective for analyzing dynamical systems such as fluid flow, Markov chains, ecological models, and matrix iterations. That's where this book comes in. This is the authoritative work on nonnormal matrices and operators, written by the authorities who made them famous. Each of the sixty sections is written as a self-contained essay. Each document is a lavishly illustrated introductory survey of its topic, complete with beautiful numerical experiments and all the right references. The breadth of included topics and the numerous applications that provide links between fields will make this an essential reference in mathematics and related sciences.

Accuracy and Stability of Numerical Algorithms

Author : Nicholas J. Higham
Publisher : SIAM
ISBN 13 : 9780898718027
Total Pages : 710 pages
Book Rating : 4.7/5 (18 download)

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Book Synopsis Accuracy and Stability of Numerical Algorithms by : Nicholas J. Higham

Download or read book Accuracy and Stability of Numerical Algorithms written by Nicholas J. Higham and published by SIAM. This book was released on 2002-01-01 with total page 710 pages. Available in PDF, EPUB and Kindle. Book excerpt: Accuracy and Stability of Numerical Algorithms gives a thorough, up-to-date treatment of the behavior of numerical algorithms in finite precision arithmetic. It combines algorithmic derivations, perturbation theory, and rounding error analysis, all enlivened by historical perspective and informative quotations. This second edition expands and updates the coverage of the first edition (1996) and includes numerous improvements to the original material. Two new chapters treat symmetric indefinite systems and skew-symmetric systems, and nonlinear systems and Newton's method. Twelve new sections include coverage of additional error bounds for Gaussian elimination, rank revealing LU factorizations, weighted and constrained least squares problems, and the fused multiply-add operation found on some modern computer architectures.

Accuracy and Stability of Numerical Algorithms

Author : Nicholas J. Higham
Publisher : SIAM
ISBN 13 : 0898715210
Total Pages : 690 pages
Book Rating : 4.8/5 (987 download)

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Book Synopsis Accuracy and Stability of Numerical Algorithms by : Nicholas J. Higham

Download or read book Accuracy and Stability of Numerical Algorithms written by Nicholas J. Higham and published by SIAM. This book was released on 2002-08-01 with total page 690 pages. Available in PDF, EPUB and Kindle. Book excerpt: Accuracy and Stability of Numerical Algorithms gives a thorough, up-to-date treatment of the behavior of numerical algorithms in finite precision arithmetic. It combines algorithmic derivations, perturbation theory, and rounding error analysis, all enlivened by historical perspective and informative quotations. This second edition expands and updates the coverage of the first edition (1996) and includes numerous improvements to the original material. Two new chapters treat symmetric indefinite systems and skew-symmetric systems, and nonlinear systems and Newton's method. Twelve new sections include coverage of additional error bounds for Gaussian elimination, rank revealing LU factorizations, weighted and constrained least squares problems, and the fused multiply-add operation found on some modern computer architectures.

Enabling Technologies for Computational Science

Author : Elias N. Houstis
Publisher : Springer Science & Business Media
ISBN 13 : 1461545412
Total Pages : 399 pages
Book Rating : 4.4/5 (615 download)

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Book Synopsis Enabling Technologies for Computational Science by : Elias N. Houstis

Download or read book Enabling Technologies for Computational Science written by Elias N. Houstis and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 399 pages. Available in PDF, EPUB and Kindle. Book excerpt: Enabling Technologies for Computational Science assesses future application computing needs, identifies research directions in problem-solving environments (PSEs), addresses multi-disciplinary environments operating on the Web, proposes methodologies and software architectures for building adaptive and human-centered PSEs, and describes the role of symbolic computing in scientific and engineering PSEs. The book also includes an extensive bibliography of over 400 references. Enabling Technologies for Computational Science illustrates the extremely broad and interdisciplinary nature of the creation and application of PSEs. Authors represent academia, government laboratories and industry, and come from eight distinct disciplines (chemical engineering, computer science, ecology, electrical engineering, mathematics, mechanical engineering, psychology and wood sciences). This breadth and diversity extends into the computer science aspects of PSEs. These papers deal with topics such as artificial intelligence, computer-human interaction, control, data mining, graphics, language design and implementation, networking, numerical analysis, performance evaluation, and symbolic computing. Enabling Technologies for Computational Science provides an assessment of the state of the art and a road map to the future in the area of problem-solving environments for scientific computing. This book is suitable as a reference for scientists from a variety of disciplines interested in using PSEs for their research.

Continuum Mechanics, Applied Mathematics and Scientific Computing: Godunov's Legacy

Author : Gennadii V. Demidenko
Publisher : Springer Nature
ISBN 13 : 3030388700
Total Pages : 378 pages
Book Rating : 4.0/5 (33 download)

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Book Synopsis Continuum Mechanics, Applied Mathematics and Scientific Computing: Godunov's Legacy by : Gennadii V. Demidenko

Download or read book Continuum Mechanics, Applied Mathematics and Scientific Computing: Godunov's Legacy written by Gennadii V. Demidenko and published by Springer Nature. This book was released on 2020-04-03 with total page 378 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is a liber amicorum to Professor Sergei Konstantinovich Godunov and gathers contributions by renowned scientists in honor of his 90th birthday. The contributions address those fields that Professor Godunov is most famous for: differential and difference equations, partial differential equations, equations of mathematical physics, mathematical modeling, difference schemes, advanced computational methods for hyperbolic equations, computational methods for linear algebra, and mathematical problems in continuum mechanics.

Applied Numerical Linear Algebra

Author : James W. Demmel
Publisher : SIAM
ISBN 13 : 1611971446
Total Pages : 427 pages
Book Rating : 4.6/5 (119 download)

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Book Synopsis Applied Numerical Linear Algebra by : James W. Demmel

Download or read book Applied Numerical Linear Algebra written by James W. Demmel and published by SIAM. This book was released on 1997-01-01 with total page 427 pages. Available in PDF, EPUB and Kindle. Book excerpt: Designed for use by first-year graduate students from a variety of engineering and scientific disciplines, this comprehensive textbook covers the solution of linear systems, least squares problems, eigenvalue problems, and the singular value decomposition. The author, who helped design the widely-used LAPACK and ScaLAPACK linear algebra libraries, draws on this experience to present state-of-the-art techniques for these problems, including recommendations of which algorithms to use in a variety of practical situations. Algorithms are derived in a mathematically illuminating way, including condition numbers and error bounds. Direct and iterative algorithms, suitable for dense and sparse matrices, are discussed. Algorithm design for modern computer architectures, where moving data is often more expensive than arithmetic operations, is discussed in detail, using LAPACK as an illustration. There are many numerical examples throughout the text and in the problems at the ends of chapters, most of which are written in Matlab and are freely available on the Web. Demmel discusses several current research topics, making students aware of both the lively research taking place and connections to other parts of numerical analysis, mathematics, and computer science. Some of this material is developed in questions at the end of each chapter, which are marked Easy, Medium, or Hard according to their difficulty. Some questions are straightforward, supplying proofs of lemmas used in the text. Others are more difficult theoretical or computing problems. Questions involving significant amounts of programming are marked Programming. The computing questions mainly involve Matlab programming, and others involve retrieving, using, and perhaps modifying LAPACK code from NETLIB.

Inverse and Ill-posed Problems

Author : Sergey I. Kabanikhin
Publisher : Walter de Gruyter
ISBN 13 : 3110224011
Total Pages : 476 pages
Book Rating : 4.1/5 (12 download)

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Book Synopsis Inverse and Ill-posed Problems by : Sergey I. Kabanikhin

Download or read book Inverse and Ill-posed Problems written by Sergey I. Kabanikhin and published by Walter de Gruyter. This book was released on 2011-12-23 with total page 476 pages. Available in PDF, EPUB and Kindle. Book excerpt: The theory of ill-posed problems originated in an unusual way. As a rule, a new concept is a subject in which its creator takes a keen interest. The concept of ill-posed problems was introduced by Hadamard with the comment that these problems are physically meaningless and not worthy of the attention of serious researchers. Despite Hadamard's pessimistic forecasts, however, his unloved "child" has turned into a powerful theory whose results are used in many fields of pure and applied mathematics. What is the secret of its success? The answer is clear. Ill-posed problems occur everywhere and it is unreasonable to ignore them. Unlike ill-posed problems, inverse problems have no strict mathematical definition. In general, they can be described as the task of recovering a part of the data of a corresponding direct (well-posed) problem from information about its solution. Inverse problems were first encountered in practice and are mostly ill-posed. The urgent need for their solution, especially in geological exploration and medical diagnostics, has given powerful impetus to the development of the theory of ill-posed problems. Nowadays, the terms "inverse problem" and "ill-posed problem" are inextricably linked to each other. Inverse and ill-posed problems are currently attracting great interest. A vast literature is devoted to these problems, making it necessary to systematize the accumulated material. This book is the first small step in that direction. We propose a classification of inverse problems according to the type of equation, unknowns and additional information. We consider specific problems from a single position and indicate relationships between them. The problems relate to different areas of mathematics, such as linear algebra, theory of integral equations, integral geometry, spectral theory and mathematical physics. We give examples of applied problems that can be studied using the techniques we describe. This book was conceived as a textbook on the foundations of the theory of inverse and ill-posed problems for university students. The author's intention was to explain this complex material in the most accessible way possible. The monograph is aimed primarily at those who are just beginning to get to grips with inverse and ill-posed problems but we hope that it will be useful to anyone who is interested in the subject.

Applied Parallel and Scientific Computing

Author : Kristján Jónasson
Publisher : Springer Science & Business Media
ISBN 13 : 3642281508
Total Pages : 364 pages
Book Rating : 4.6/5 (422 download)

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Book Synopsis Applied Parallel and Scientific Computing by : Kristján Jónasson

Download or read book Applied Parallel and Scientific Computing written by Kristján Jónasson and published by Springer Science & Business Media. This book was released on 2012-02-13 with total page 364 pages. Available in PDF, EPUB and Kindle. Book excerpt: The two volume set LNCS 7133 and LNCS 7134 constitutes the thoroughly refereed post-conference proceedings of the 10th International Conference on Applied Parallel and Scientific Computing, PARA 2010, held in Reykjavík, Iceland, in June 2010. These volumes contain three keynote lectures, 29 revised papers and 45 minisymposia presentations arranged on the following topics: cloud computing, HPC algorithms, HPC programming tools, HPC in meteorology, parallel numerical algorithms, parallel computing in physics, scientific computing tools, HPC software engineering, simulations of atomic scale systems, tools and environments for accelerator based computational biomedicine, GPU computing, high performance computing interval methods, real-time access and processing of large data sets, linear algebra algorithms and software for multicore and hybrid architectures in honor of Fred Gustavson on his 75th birthday, memory and multicore issues in scientific computing - theory and praxis, multicore algorithms and implementations for application problems, fast PDE solvers and a posteriori error estimates, and scalable tools for high performance computing.

A Theoretical Introduction to Numerical Analysis

Author : Victor S. Ryaben'kii
Publisher : CRC Press
ISBN 13 : 1000738280
Total Pages : 564 pages
Book Rating : 4.0/5 (7 download)

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Book Synopsis A Theoretical Introduction to Numerical Analysis by : Victor S. Ryaben'kii

Download or read book A Theoretical Introduction to Numerical Analysis written by Victor S. Ryaben'kii and published by CRC Press. This book was released on 2006-11-02 with total page 564 pages. Available in PDF, EPUB and Kindle. Book excerpt: A Theoretical Introduction to Numerical Analysis presents the general methodology and principles of numerical analysis, illustrating these concepts using numerical methods from real analysis, linear algebra, and differential equations. The book focuses on how to efficiently represent mathematical models for computer-based study. An access

Principles of Modern Radar Missile Seekers

Author : Evgeny Markin
Publisher : Artech House
ISBN 13 : 1630817783
Total Pages : 320 pages
Book Rating : 4.6/5 (38 download)

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Book Synopsis Principles of Modern Radar Missile Seekers by : Evgeny Markin

Download or read book Principles of Modern Radar Missile Seekers written by Evgeny Markin and published by Artech House. This book was released on 2022-02-28 with total page 320 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book gives you an in-depth look into the critical function of interference shielding for onboard radar of anti-aircraft missile systems. Intended for radar engineers and technicians specializing in anti-aircraft defense, the book reviews today’s military and geo-political threats, helps you understand the functional needs of the various radar and anti-missile systems to meet those threats, and synthesizes considerations for devising practical and effective protection against interferences that affect the homing heads of anti-aircraft guided missiles. Three problematic interferences are presented and discussed in detail: polarization interference; interference to the sidelobe of onboard antennas; and interference from two points in space, including interference reflected from the earth (water) surface. The book covers the basic principles of radiolocation, including monopulse radars, and gives insight into the fundamental functional units of anti-aircraft missiles and surface-to-air missile systems. The book presents guidance methods, systems of direction finding, problems on firing over the horizon, and questions of accuracy and resolution – all important for better addressing solutions of interference shielding. You will learn how to estimate the stability of target auto-tracking under conditions of cited interferences, and better assess existing limitations on firing over the horizon by a long-range antiaircraft system, as well as hypersonic targets and satellites. This is a unique and valuable resource for engineers and technicians who are involved in the design and development of anti-aircraft guided missile systems, with special emphasis on interference immunity and protection. It can also be used as a textbook in advanced radar technology coursework and seminars.

J.UCS The Journal of Universal Computer Science

Author : Hermann Maurer
Publisher : Springer Science & Business Media
ISBN 13 : 3642803504
Total Pages : 866 pages
Book Rating : 4.6/5 (428 download)

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Book Synopsis J.UCS The Journal of Universal Computer Science by : Hermann Maurer

Download or read book J.UCS The Journal of Universal Computer Science written by Hermann Maurer and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 866 pages. Available in PDF, EPUB and Kindle. Book excerpt: J.UCS is the electronic journal that covers all areas of computer science. The high quality of all accepted papers is ensured by a strict review process and an international editorial board of distinguished computer scientists. The online journal J.UCS is a prototype for modern electronic publishing. Distributed via the Internet, it supports all the search and navigation tools of advanced online systems. This first annual print and CD-ROM archive edition contains all articles published online in J.UCS during 1995. It allows easy and durable access without logging onto the Internet. Uniform citation of papers is guaranteed by identical page numbering and layout of all versions. J.UCS is based on HyperWave (formerly Hyper-G), a networked hypermedia information system compatible with other systems.

The Graduate Student’s Guide to Numerical Analysis ’98

Author : Mark Ainsworth
Publisher : Springer Science & Business Media
ISBN 13 : 3662039729
Total Pages : 262 pages
Book Rating : 4.6/5 (62 download)

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Book Synopsis The Graduate Student’s Guide to Numerical Analysis ’98 by : Mark Ainsworth

Download or read book The Graduate Student’s Guide to Numerical Analysis ’98 written by Mark Ainsworth and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 262 pages. Available in PDF, EPUB and Kindle. Book excerpt: Detailed lecture notes on six topics at the forefront of current research in numerical analysis and applied mathematics, with each set of notes presenting a self-contained guide to a current research area and supplemented by an extensive bibliography. In addition, most of the notes contain detailed proofs of the key results. They start from a level suitable for first year graduates in applied mathematics, mathematical analysis or numerical analysis, and proceed to current research topics. Readers will thus quickly gain an insight into the important results and techniques in each area without recourse to the large research literature. Current (unsolved) problems are also described, and directions for future research given.