Algorithms For Large Scale Linear Algebraic Systems

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Parallel Algorithms for Optimal Control of Large Scale Linear Systems

Author : Zoran Gajic
Publisher : Springer Science & Business Media
ISBN 13 : 144713219X
Total Pages : 462 pages
Book Rating : 4.4/5 (471 download)

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Book Synopsis Parallel Algorithms for Optimal Control of Large Scale Linear Systems by : Zoran Gajic

Download or read book Parallel Algorithms for Optimal Control of Large Scale Linear Systems written by Zoran Gajic and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 462 pages. Available in PDF, EPUB and Kindle. Book excerpt: Parallel Algorithms for Optimal Control of Large Scale Linear Systems is a comprehensive presentation for both linear and bilinear systems. The parallel algorithms presented in this book are applicable to a wider class of practical systems than those served by traditional methods for large scale singularly perturbed and weakly coupled systems based on the power-series expansion methods. It is intended for scientists and advance graduate students in electrical engineering and computer science who deal with parallel algorithms and control systems, especially large scale systems. The material presented is both comprehensive and unique.

Linear Algebra for Large Scale and Real-Time Applications

Author : M.S. Moonen
Publisher : Springer Science & Business Media
ISBN 13 : 9401581967
Total Pages : 434 pages
Book Rating : 4.4/5 (15 download)

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Book Synopsis Linear Algebra for Large Scale and Real-Time Applications by : M.S. Moonen

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

Iterative Methods for Sparse Linear Systems

Author : Yousef Saad
Publisher : SIAM
ISBN 13 : 0898715342
Total Pages : 537 pages
Book Rating : 4.8/5 (987 download)

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Book Synopsis Iterative Methods for Sparse Linear Systems by : Yousef Saad

Download or read book Iterative Methods for Sparse Linear Systems written by Yousef Saad and published by SIAM. This book was released on 2003-04-01 with total page 537 pages. Available in PDF, EPUB and Kindle. Book excerpt: Mathematics of Computing -- General.

Krylov Solvers for Linear Algebraic Systems

Author : Charles George Broyden
Publisher : Elsevier
ISBN 13 : 0080478875
Total Pages : 343 pages
Book Rating : 4.0/5 (84 download)

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Book Synopsis Krylov Solvers for Linear Algebraic Systems by : Charles George Broyden

Download or read book Krylov Solvers for Linear Algebraic Systems written by Charles George Broyden and published by Elsevier. This book was released on 2004-09-08 with total page 343 pages. Available in PDF, EPUB and Kindle. Book excerpt: The first four chapters of this book give a comprehensive and unified theory of the Krylov methods. Many of these are shown to be particular examples ofthe block conjugate-gradient algorithm and it is this observation thatpermits the unification of the theory. The two major sub-classes of thosemethods, the Lanczos and the Hestenes-Stiefel, are developed in parallel asnatural generalisations of the Orthodir (GCR) and Orthomin algorithms. Theseare themselves based on Arnoldi's algorithm and a generalised Gram-Schmidtalgorithm and their properties, in particular their stability properties,are determined by the two matrices that define the block conjugate-gradientalgorithm. These are the matrix of coefficients and the preconditioningmatrix.In Chapter 5 the"transpose-free" algorithms based on the conjugate-gradient squared algorithm are presented while Chapter 6 examines the various ways in which the QMR technique has been exploited. Look-ahead methods and general block methods are dealt with in Chapters 7 and 8 while Chapter 9 is devoted to error analysis of two basic algorithms.In Chapter 10 the results of numerical testing of the more important algorithms in their basic forms (i.e. without look-ahead or preconditioning) are presented and these are related to the structure of the algorithms and the general theory. Graphs illustrating the performances of various algorithm/problem combinations are given via a CD-ROM.Chapter 11, by far the longest, gives a survey of preconditioning techniques. These range from the old idea of polynomial preconditioning via SOR and ILU preconditioning to methods like SpAI, AInv and the multigrid methods that were developed specifically for use with parallel computers. Chapter 12 is devoted to dual algorithms like Orthores and the reverse algorithms of Hegedus. Finally certain ancillary matters like reduction to Hessenberg form, Chebychev polynomials and the companion matrix are described in a series of appendices.·comprehensive and unified approach·up-to-date chapter on preconditioners·complete theory of stability·includes dual and reverse methods·comparison of algorithms on CD-ROM·objective assessment of algorithms

Fast Direct Solvers for Elliptic PDEs

Author : Per-Gunnar Martinsson
Publisher : SIAM
ISBN 13 : 1611976049
Total Pages : 332 pages
Book Rating : 4.6/5 (119 download)

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Book Synopsis Fast Direct Solvers for Elliptic PDEs by : Per-Gunnar Martinsson

Download or read book Fast Direct Solvers for Elliptic PDEs written by Per-Gunnar Martinsson and published by SIAM. This book was released on 2019-12-16 with total page 332 pages. Available in PDF, EPUB and Kindle. Book excerpt: Fast solvers for elliptic PDEs form a pillar of scientific computing. They enable detailed and accurate simulations of electromagnetic fields, fluid flows, biochemical processes, and much more. This textbook provides an introduction to fast solvers from the point of view of integral equation formulations, which lead to unparalleled accuracy and speed in many applications. The focus is on fast algorithms for handling dense matrices that arise in the discretization of integral operators, such as the fast multipole method and fast direct solvers. While the emphasis is on techniques for dense matrices, the text also describes how similar techniques give rise to linear complexity algorithms for computing the inverse or the LU factorization of a sparse matrix resulting from the direct discretization of an elliptic PDE. This is the first textbook to detail the active field of fast direct solvers, introducing readers to modern linear algebraic techniques for accelerating computations, such as randomized algorithms, interpolative decompositions, and data-sparse hierarchical matrix representations. Written with an emphasis on mathematical intuition rather than theoretical details, it is richly illustrated and provides pseudocode for all key techniques. Fast Direct Solvers for Elliptic PDEs is appropriate for graduate students in applied mathematics and scientific computing, engineers and scientists looking for an accessible introduction to integral equation methods and fast solvers, and researchers in computational mathematics who want to quickly catch up on recent advances in randomized algorithms and techniques for working with data-sparse matrices.

Dimension Reduction of Large-Scale Systems

Author : Peter Benner
Publisher : Springer Science & Business Media
ISBN 13 : 3540279091
Total Pages : 397 pages
Book Rating : 4.5/5 (42 download)

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Book Synopsis Dimension Reduction of Large-Scale Systems by : Peter Benner

Download or read book Dimension Reduction of Large-Scale Systems written by Peter Benner and published by Springer Science & Business Media. This book was released on 2006-03-30 with total page 397 pages. Available in PDF, EPUB and Kindle. Book excerpt: In the past decades, model reduction has become an ubiquitous tool in analysis and simulation of dynamical systems, control design, circuit simulation, structural dynamics, CFD, and many other disciplines dealing with complex physical models. The aim of this book is to survey some of the most successful model reduction methods in tutorial style articles and to present benchmark problems from several application areas for testing and comparing existing and new algorithms. As the discussed methods have often been developed in parallel in disconnected application areas, the intention of the mini-workshop in Oberwolfach and its proceedings is to make these ideas available to researchers and practitioners from all these different disciplines.

Large Scale Linear and Integer Optimization: A Unified Approach

Author : Richard Kipp Martin
Publisher : Springer Science & Business Media
ISBN 13 : 1461549752
Total Pages : 739 pages
Book Rating : 4.4/5 (615 download)

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Book Synopsis Large Scale Linear and Integer Optimization: A Unified Approach by : Richard Kipp Martin

Download or read book Large Scale Linear and Integer Optimization: A Unified Approach written by Richard Kipp Martin and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 739 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is a textbook about linear and integer linear optimization. There is a growing need in industries such as airline, trucking, and financial engineering to solve very large linear and integer linear optimization problems. Building these models requires uniquely trained individuals. Not only must they have a thorough understanding of the theory behind mathematical programming, they must have substantial knowledge of how to solve very large models in today's computing environment. The major goal of the book is to develop the theory of linear and integer linear optimization in a unified manner and then demonstrate how to use this theory in a modern computing environment to solve very large real world problems. After presenting introductory material in Part I, Part II of this book is de voted to the theory of linear and integer linear optimization. This theory is developed using two simple, but unifying ideas: projection and inverse projec tion. Through projection we take a system of linear inequalities and replace some of the variables with additional linear inequalities. Inverse projection, the dual of this process, involves replacing linear inequalities with additional variables. Fundamental results such as weak and strong duality, theorems of the alternative, complementary slackness, sensitivity analysis, finite basis the orems, etc. are all explained using projection or inverse projection. Indeed, a unique feature of this book is that these fundamental results are developed and explained before the simplex and interior point algorithms are presented.

Graph Algorithms in the Language of Linear Algebra

Author : Jeremy Kepner
Publisher : SIAM
ISBN 13 : 9780898719918
Total Pages : 388 pages
Book Rating : 4.7/5 (199 download)

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Book Synopsis Graph Algorithms in the Language of Linear Algebra by : Jeremy Kepner

Download or read book Graph Algorithms in the Language of Linear Algebra written by Jeremy Kepner and published by SIAM. This book was released on 2011-01-01 with total page 388 pages. Available in PDF, EPUB and Kindle. Book excerpt: The current exponential growth in graph data has forced a shift to parallel computing for executing graph algorithms. Implementing parallel graph algorithms and achieving good parallel performance have proven difficult. This book addresses these challenges by exploiting the well-known duality between a canonical representation of graphs as abstract collections of vertices and edges and a sparse adjacency matrix representation. This linear algebraic approach is widely accessible to scientists and engineers who may not be formally trained in computer science. The authors show how to leverage existing parallel matrix computation techniques and the large amount of software infrastructure that exists for these computations to implement efficient and scalable parallel graph algorithms. The benefits of this approach are reduced algorithmic complexity, ease of implementation, and improved performance.

Handbook of Linear Algebra

Author : Leslie Hogben
Publisher : CRC Press
ISBN 13 : 1420010573
Total Pages : 1402 pages
Book Rating : 4.4/5 (2 download)

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Book Synopsis Handbook of Linear Algebra by : Leslie Hogben

Download or read book Handbook of Linear Algebra written by Leslie Hogben and published by CRC Press. This book was released on 2006-11-02 with total page 1402 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Handbook of Linear Algebra provides comprehensive coverage of linear algebra concepts, applications, and computational software packages in an easy-to-use handbook format. The esteemed international contributors guide you from the very elementary aspects of the subject to the frontiers of current research. The book features an accessibl

Handbook of Linear Algebra, Second Edition

Author : Leslie Hogben
Publisher : CRC Press
ISBN 13 : 1466507284
Total Pages : 1906 pages
Book Rating : 4.4/5 (665 download)

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Book Synopsis Handbook of Linear Algebra, Second Edition by : Leslie Hogben

Download or read book Handbook of Linear Algebra, Second Edition written by Leslie Hogben and published by CRC Press. This book was released on 2013-11-26 with total page 1906 pages. Available in PDF, EPUB and Kindle. Book excerpt: With a substantial amount of new material, the Handbook of Linear Algebra, Second Edition provides comprehensive coverage of linear algebra concepts, applications, and computational software packages in an easy-to-use format. It guides you from the very elementary aspects of the subject to the frontiers of current research. Along with revisions and updates throughout, the second edition of this bestseller includes 20 new chapters. New to the Second Edition Separate chapters on Schur complements, additional types of canonical forms, tensors, matrix polynomials, matrix equations, special types of matrices, generalized inverses, matrices over finite fields, invariant subspaces, representations of quivers, and spectral sets New chapters on combinatorial matrix theory topics, such as tournaments, the minimum rank problem, and spectral graph theory, as well as numerical linear algebra topics, including algorithms for structured matrix computations, stability of structured matrix computations, and nonlinear eigenvalue problems More chapters on applications of linear algebra, including epidemiology and quantum error correction New chapter on using the free and open source software system Sage for linear algebra Additional sections in the chapters on sign pattern matrices and applications to geometry Conjectures and open problems in most chapters on advanced topics Highly praised as a valuable resource for anyone who uses linear algebra, the first edition covered virtually all aspects of linear algebra and its applications. This edition continues to encompass the fundamentals of linear algebra, combinatorial and numerical linear algebra, and applications of linear algebra to various disciplines while also covering up-to-date software packages for linear algebra computations.

Linear Algebra: Systems of Linear Equations

Author : N.B. Singh
Publisher : N.B. Singh
ISBN 13 :
Total Pages : 175 pages
Book Rating : 4./5 ( download)

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Book Synopsis Linear Algebra: Systems of Linear Equations by : N.B. Singh

Download or read book Linear Algebra: Systems of Linear Equations written by N.B. Singh and published by N.B. Singh. This book was released on with total page 175 pages. Available in PDF, EPUB and Kindle. Book excerpt: "Linear Algebra: Systems of Linear Equations" is an introductory textbook designed for absolute beginners seeking to grasp the fundamental concepts of linear algebra. Through clear explanations, practical examples, and step-by-step guidance, this book demystifies the principles of systems of linear equations, equipping readers with essential skills to analyze and solve real-world problems using matrix operations, vector spaces, and foundational algebraic techniques. Ideal for students and self-learners alike, it aims to foster a deep understanding of linear algebra's relevance and applicability across various disciplines.

Numerical Algorithms

Author : Justin Solomon
Publisher : CRC Press
ISBN 13 : 1482251892
Total Pages : 400 pages
Book Rating : 4.4/5 (822 download)

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Book Synopsis Numerical Algorithms by : Justin Solomon

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

Hierarchical Matrices: Algorithms and Analysis

Author : Wolfgang Hackbusch
Publisher : Springer
ISBN 13 : 3662473240
Total Pages : 532 pages
Book Rating : 4.6/5 (624 download)

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Book Synopsis Hierarchical Matrices: Algorithms and Analysis by : Wolfgang Hackbusch

Download or read book Hierarchical Matrices: Algorithms and Analysis written by Wolfgang Hackbusch and published by Springer. This book was released on 2015-12-21 with total page 532 pages. Available in PDF, EPUB and Kindle. Book excerpt: This self-contained monograph presents matrix algorithms and their analysis. The new technique enables not only the solution of linear systems but also the approximation of matrix functions, e.g., the matrix exponential. Other applications include the solution of matrix equations, e.g., the Lyapunov or Riccati equation. The required mathematical background can be found in the appendix. The numerical treatment of fully populated large-scale matrices is usually rather costly. However, the technique of hierarchical matrices makes it possible to store matrices and to perform matrix operations approximately with almost linear cost and a controllable degree of approximation error. For important classes of matrices, the computational cost increases only logarithmically with the approximation error. The operations provided include the matrix inversion and LU decomposition. Since large-scale linear algebra problems are standard in scientific computing, the subject of hierarchical matrices is of interest to scientists in computational mathematics, physics, chemistry and engineering.

Numerical methods for scientists and engineers

Author : H. M. Antia
Publisher : Springer
ISBN 13 : 9386279525
Total Pages : 888 pages
Book Rating : 4.3/5 (862 download)

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Book Synopsis Numerical methods for scientists and engineers by : H. M. Antia

Download or read book Numerical methods for scientists and engineers written by H. M. Antia and published by Springer. This book was released on 2012-11-15 with total page 888 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents an exhaustive and in-depth exposition of the various numerical methods used in scientific and engineering computations. It emphasises the practical aspects of numerical computation and discusses various techniques in sufficient detail to enable their implementation in solving a wide range of problems. The main addition in the third edition is a new Chapter on Statistical Inferences. There is also some addition and editing in the next chapter on Approximations. With this addition 12 new programs have also been added.

Algorithms for Sparse Linear Systems

Author : Jennifer Scott
Publisher : Springer Nature
ISBN 13 : 3031258207
Total Pages : 254 pages
Book Rating : 4.0/5 (312 download)

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Book Synopsis Algorithms for Sparse Linear Systems by : Jennifer Scott

Download or read book Algorithms for Sparse Linear Systems written by Jennifer Scott and published by Springer Nature. This book was released on 2023-04-29 with total page 254 pages. Available in PDF, EPUB and Kindle. Book excerpt: Large sparse linear systems of equations are ubiquitous in science, engineering and beyond. This open access monograph focuses on factorization algorithms for solving such systems. It presents classical techniques for complete factorizations that are used in sparse direct methods and discusses the computation of approximate direct and inverse factorizations that are key to constructing general-purpose algebraic preconditioners for iterative solvers. A unified framework is used that emphasizes the underlying sparsity structures and highlights the importance of understanding sparse direct methods when developing algebraic preconditioners. Theoretical results are complemented by sparse matrix algorithm outlines. This monograph is aimed at students of applied mathematics and scientific computing, as well as computational scientists and software developers who are interested in understanding the theory and algorithms needed to tackle sparse systems. It is assumed that the reader has completed a basic course in linear algebra and numerical mathematics.

Krylov Subspace Methods

Author : Jörg Liesen
Publisher : Numerical Mathematics and Scie
ISBN 13 : 0199655413
Total Pages : 408 pages
Book Rating : 4.1/5 (996 download)

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Book Synopsis Krylov Subspace Methods by : Jörg Liesen

Download or read book Krylov Subspace Methods written by Jörg Liesen and published by Numerical Mathematics and Scie. This book was released on 2013 with total page 408 pages. Available in PDF, EPUB and Kindle. Book excerpt: Describes the principles and history behind the use of Krylov subspace methods in science and engineering. The outcome of the analysis is very practical and indicates what can and cannot be expected from the use of Krylov subspace methods, challenging some common assumptions and justifications of standard approaches.

System- and Data-Driven Methods and Algorithms

Author : Peter Benner
Publisher : Walter de Gruyter GmbH & Co KG
ISBN 13 : 3110497719
Total Pages : 346 pages
Book Rating : 4.1/5 (14 download)

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Book Synopsis System- and Data-Driven Methods and Algorithms by : Peter Benner

Download or read book System- and Data-Driven Methods and Algorithms written by Peter Benner and published by Walter de Gruyter GmbH & Co KG. This book was released on 2021-11-08 with total page 346 pages. Available in PDF, EPUB and Kindle. Book excerpt: An increasing complexity of models used to predict real-world systems leads to the need for algorithms to replace complex models with far simpler ones, while preserving the accuracy of the predictions. This two-volume handbook covers methods as well as applications. This first volume focuses on real-time control theory, data assimilation, real-time visualization, high-dimensional state spaces and interaction of different reduction techniques.