Introduction to Numerical Linear Algebra and Optimisation

Author: Philippe G. Ciarlet,Bernadette Miara,Jean-Marie Thomas

Publisher: Cambridge University Press

ISBN: 9780521339841

Category: Computers

Page: 436

View: 6906

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Based on courses taught to advanced undergraduate students, this book offers a broad introduction to the methods of numerical linear algebra and optimization. The prerequisites are familiarity with the basic properties of matrices, finite-dimensional vector spaces and advanced calculus, and some exposure to fundamental notions from functional analysis. The book is divided into two parts. The first part deals with numerical linear algebra (numerical analysis of matrices, direct and indirect methods for solving linear systems, calculation of eigenvalues and eigenvectors) and the second, optimizations (general algorithms, linear and nonlinear programming). Summaries of basic mathematics are provided, proof of theorems are complete yet kept as simple as possible, applications from physics and mechanics are discussed, a great many exercises are included, and there is a useful guide to further reading.
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Numerical Linear Algebra

Author: Lloyd N. Trefethen,David Bau, III

Publisher: SIAM

ISBN: 0898713617

Category: Mathematics

Page: 361

View: 8710

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Numerical Linear Algebra is a concise, insightful, and elegant introduction to the field of numerical linear algebra.
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Applied Numerical Linear Algebra

Author: James W. Demmel

Publisher: SIAM

ISBN: 0898713897

Category: Mathematics

Page: 419

View: 7725

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This comprehensive textbook is designed for first-year graduate students from a variety of engineering and scientific disciplines.
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Numerical Linear Algebra

Author: Holger Wendland

Publisher: Cambridge University Press

ISBN: 1107147131

Category: Computers

Page: 418

View: 1484

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This self-contained introduction to numerical linear algebra provides a comprehensive, yet concise, overview of the subject. It includes standard material such as direct methods for solving linear systems and least-squares problems, error, stability and conditioning, basic iterative methods and the calculation of eigenvalues. Later chapters cover more advanced material, such as Krylov subspace methods, multigrid methods, domain decomposition methods, multipole expansions, hierarchical matrices and compressed sensing. The book provides rigorous mathematical proofs throughout, and gives algorithms in general-purpose language-independent form. Requiring only a solid knowledge in linear algebra and basic analysis, this book will be useful for applied mathematicians, engineers, computer scientists, and all those interested in efficiently solving linear problems.
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Numerical Linear Algebra

Author: Grégoire Allaire,Sidi Mahmoud Kaber

Publisher: Springer Science & Business Media

ISBN: 9780387689180

Category: Mathematics

Page: 271

View: 1447

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This book distinguishes itself from the many other textbooks on the topic of linear algebra by including mathematical and computational chapters along with examples and exercises with Matlab. In recent years, the use of computers in many areas of engineering and science has made it essential for students to get training in numerical methods and computer programming. Here, the authors use both Matlab and SciLab software as well as covering core standard material. It is intended for libraries; scientists and researchers; pharmaceutical industry.
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Numerical Linear Algebra with Applications

Using MATLAB

Author: William Ford

Publisher: Academic Press

ISBN: 0123947847

Category: Mathematics

Page: 628

View: 933

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Numerical Linear Algebra with Applications is designed for those who want to gain a practical knowledge of modern computational techniques for the numerical solution of linear algebra problems, using MATLAB as the vehicle for computation. The book contains all the material necessary for a first year graduate or advanced undergraduate course on numerical linear algebra with numerous applications to engineering and science. With a unified presentation of computation, basic algorithm analysis, and numerical methods to compute solutions, this book is ideal for solving real-world problems. The text consists of six introductory chapters that thoroughly provide the required background for those who have not taken a course in applied or theoretical linear algebra. It explains in great detail the algorithms necessary for the accurate computation of the solution to the most frequently occurring problems in numerical linear algebra. In addition to examples from engineering and science applications, proofs of required results are provided without leaving out critical details. The Preface suggests ways in which the book can be used with or without an intensive study of proofs. This book will be a useful reference for graduate or advanced undergraduate students in engineering, science, and mathematics. It will also appeal to professionals in engineering and science, such as practicing engineers who want to see how numerical linear algebra problems can be solved using a programming language such as MATLAB, MAPLE, or Mathematica. Six introductory chapters that thoroughly provide the required background for those who have not taken a course in applied or theoretical linear algebra Detailed explanations and examples A through discussion of the algorithms necessary for the accurate computation of the solution to the most frequently occurring problems in numerical linear algebra Examples from engineering and science applications
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Numerical Linear Algebra and Applications, Second Edition

Author: Biswa Nath Datta

Publisher: SIAM

ISBN: 0898717655

Category: Algebras, Linear

Page: 530

View: 9698

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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.
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Numerical Linear Algebra

A Concise Introduction with MATLAB and Julia

Author: Folkmar Bornemann

Publisher: Springer

ISBN: 3319742221

Category: Mathematics

Page: 153

View: 940

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This book offers an introduction to the algorithmic-numerical thinking using basic problems of linear algebra. By focusing on linear algebra, it ensures a stronger thematic coherence than is otherwise found in introductory lectures on numerics. The book highlights the usefulness of matrix partitioning compared to a component view, leading not only to a clearer notation and shorter algorithms, but also to significant runtime gains in modern computer architectures. The algorithms and accompanying numerical examples are given in the programming environment MATLAB, and additionally – in an appendix – in the future-oriented, freely accessible programming language Julia. This book is suitable for a two-hour lecture on numerical linear algebra from the second semester of a bachelor's degree in mathematics.
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Numerical Linear Algebra for High-performance Computers

Author: Jack J. Dongarra,Iain S. Duff,Danny C. Sorensen,Henk A. van der Vorst

Publisher: SIAM

ISBN: 9780898719611

Category: Algebras, Linear

Page: 342

View: 7234

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This book presents a unified treatment of recently developed techniques and current understanding about solving systems of linear equations and large scale eigenvalue problems on high-performance computers. It provides a rapid introduction to the world of vector and parallel processing for these linear algebra applications. Topics include major elements of advanced-architecture computers and their performance, recent algorithmic development, and software for direct solution of dense matrix problems, direct solution of sparse systems of equations, iterative solution of sparse systems of equations, and solution of large sparse eigenvalue problems.
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Numerical Linear Algebra

Proceedings of the Conference in Numerical Linear Algebra and Scientific Computation, Kent (Ohio), USA March 13-14, 1992

Author: Lothar Reichel,Arden Ruttan,Richard S. Varga

Publisher: Walter de Gruyter

ISBN: 3110857650

Category: Mathematics

Page: 206

View: 5190

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The series is aimed specifically at publishing peer reviewed reviews and contributions presented at workshops and conferences. Each volume is associated with a particular conference, symposium or workshop. These events cover various topics within pure and applied mathematics and provide up-to-date coverage of new developments, methods and applications.
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