Numerical Linear Algebra And Matrix Factorizations

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Numerical Linear Algebra and Matrix Factorizations

Tom Lyche
Numerical Linear Algebra and Matrix Factorizations Book PDF

Author : Tom Lyche
Publisher : Springer Nature
Page : 376 pages
File Size : 41,7 Mb
Release : 2020-03-02
Category : Mathematics
ISBN : 9783030364687

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Numerical Linear Algebra and Matrix Factorizations by Tom Lyche Pdf

After reading this book, students should be able to analyze computational problems in linear algebra such as linear systems, least squares- and eigenvalue problems, and to develop their own algorithms for solving them. Since these problems can be large and difficult to handle, much can be gained by understanding and taking advantage of special structures. This in turn requires a good grasp of basic numerical linear algebra and matrix factorizations. Factoring a matrix into a product of simpler matrices is a crucial tool in numerical linear algebra, because it allows us to tackle complex problems by solving a sequence of easier ones. The main characteristics of this book are as follows: It is self-contained, only assuming that readers have completed first-year calculus and an introductory course on linear algebra, and that they have some experience with solving mathematical problems on a computer. The book provides detailed proofs of virtually all results. Further, its respective parts can be used independently, making it suitable for self-study. The book consists of 15 chapters, divided into five thematically oriented parts. The chapters are designed for a one-week-per-chapter, one-semester course. To facilitate self-study, an introductory chapter includes a brief review of linear algebra.

Exercises in Numerical Linear Algebra and Matrix Factorizations

Tom Lyche,Georg Muntingh,Øyvind Ryan
Exercises in Numerical Linear Algebra and Matrix Factorizations Book PDF

Author : Tom Lyche,Georg Muntingh,Øyvind Ryan
Publisher : Springer Nature
Page : 265 pages
File Size : 49,8 Mb
Release : 2020-11-02
Category : Mathematics
ISBN : 9783030597894

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Exercises in Numerical Linear Algebra and Matrix Factorizations by Tom Lyche,Georg Muntingh,Øyvind Ryan Pdf

To put the world of linear algebra to advanced use, it is not enough to merely understand the theory; there is a significant gap between the theory of linear algebra and its myriad expressions in nearly every computational domain. To bridge this gap, it is essential to process the theory by solving many exercises, thus obtaining a firmer grasp of its diverse applications. Similarly, from a theoretical perspective, diving into the literature on advanced linear algebra often reveals more and more topics that are deferred to exercises instead of being treated in the main text. As exercises grow more complex and numerous, it becomes increasingly important to provide supporting material and guidelines on how to solve them, supporting students’ learning process. This book provides precisely this type of supporting material for the textbook “Numerical Linear Algebra and Matrix Factorizations,” published as Vol. 22 of Springer’s Texts in Computational Science and Engineering series. Instead of omitting details or merely providing rough outlines, this book offers detailed proofs, and connects the solutions to the corresponding results in the textbook. For the algorithmic exercises the utmost level of detail is provided in the form of MATLAB implementations. Both the textbook and solutions are self-contained. This book and the textbook are of similar length, demonstrating that solutions should not be considered a minor aspect when learning at advanced levels.

Nonnegative Matrix Factorization

Nicolas Gillis
Nonnegative Matrix Factorization Book PDF

Author : Nicolas Gillis
Publisher : SIAM
Page : 376 pages
File Size : 49,9 Mb
Release : 2020-12-18
Category : Mathematics
ISBN : 9781611976410

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Nonnegative Matrix Factorization by Nicolas Gillis Pdf

Nonnegative matrix factorization (NMF) in its modern form has become a standard tool in the analysis of high-dimensional data sets. This book provides a comprehensive and up-to-date account of the most important aspects of the NMF problem and is the first to detail its theoretical aspects, including geometric interpretation, nonnegative rank, complexity, and uniqueness. It explains why understanding these theoretical insights is key to using this computational tool effectively and meaningfully. Nonnegative Matrix Factorization is accessible to a wide audience and is ideal for anyone interested in the workings of NMF. It discusses some new results on the nonnegative rank and the identifiability of NMF and makes available MATLAB codes for readers to run the numerical examples presented in the book. Graduate students starting to work on NMF and researchers interested in better understanding the NMF problem and how they can use it will find this book useful. It can be used in advanced undergraduate and graduate-level courses on numerical linear algebra and on advanced topics in numerical linear algebra and requires only a basic knowledge of linear algebra and optimization.

Numerical Linear Algebra for Applications in Statistics

James E. Gentle
Numerical Linear Algebra for Applications in Statistics Book PDF

Author : James E. Gentle
Publisher : Springer Science & Business Media
Page : 244 pages
File Size : 51,6 Mb
Release : 1998-08-13
Category : Mathematics
ISBN : 0387985425

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Numerical Linear Algebra for Applications in Statistics by James E. Gentle Pdf

Accurate and efficient computer algorithms for factoring matrices, solving linear systems of equations, and extracting eigenvalues and eigenvectors. Regardless of the software system used, the book describes and gives examples of the use of modern computer software for numerical linear algebra. It begins with a discussion of the basics of numerical computations, and then describes the relevant properties of matrix inverses, factorisations, matrix and vector norms, and other topics in linear algebra. The book is essentially self- contained, with the topics addressed constituting the essential material for an introductory course in statistical computing. Numerous exercises allow the text to be used for a first course in statistical computing or as supplementary text for various courses that emphasise computations.

Numerical Linear Algebra

Lloyd N. Trefethen,David Bau, III
Numerical Linear Algebra Book PDF

Author : Lloyd N. Trefethen,David Bau, III
Publisher : SIAM
Page : 356 pages
File Size : 51,7 Mb
Release : 1997-06-01
Category : Mathematics
ISBN : 9780898713619

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Numerical Linear Algebra by Lloyd N. Trefethen,David Bau, III Pdf

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

Numerical Linear Algebra

V. SUNDARAPANDIAN
Numerical Linear Algebra Book PDF

Author : V. SUNDARAPANDIAN
Publisher : PHI Learning Pvt. Ltd.
Page : 616 pages
File Size : 55,7 Mb
Release : 2008-04-23
Category : Mathematics
ISBN : 9788120334366

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Numerical Linear Algebra by V. SUNDARAPANDIAN Pdf

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.

Numerical Linear Algebra and Applications

Biswa Nath Datta
Numerical Linear Algebra and Applications Book PDF

Author : Biswa Nath Datta
Publisher : SIAM
Page : 546 pages
File Size : 54,6 Mb
Release : 2010-01-01
Category : Mathematics
ISBN : 9780898717655

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Numerical Linear Algebra and Applications by Biswa Nath Datta Pdf

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.

Functions of Matrices

Nicholas J. Higham
Functions of Matrices Book PDF

Author : Nicholas J. Higham
Publisher : SIAM
Page : 431 pages
File Size : 55,6 Mb
Release : 2008-09-11
Category : Mathematics
ISBN : 9780898716467

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Functions of Matrices by Nicholas J. Higham Pdf

“This superb book is timely and is written with great attention paid to detail, particularly in its referencing of the literature. The book has a wonderful blend of theory and code (MATLAB®) so will be useful both to nonexperts and to experts in the field.” — Alan Laub, Professor, University of California, Los Angeles The only book devoted exclusively to matrix functions, this research monograph gives a thorough treatment of the theory of matrix functions and numerical methods for computing them. The author's elegant presentation focuses on the equivalent definitions of f(A) via the Jordan canonical form, polynomial interpolation, and the Cauchy integral formula, and features an emphasis on results of practical interest and an extensive collection of problems and solutions. Functions of Matrices: Theory and Computation is more than just a monograph on matrix functions; its wide-ranging content—including an overview of applications, historical references, and miscellaneous results, tricks, and techniques with an f(A) connection—makes it useful as a general reference in numerical linear algebra.Other key features of the book include development of the theory of conditioning and properties of the Fréchet derivative; an emphasis on the Schur decomposition, the block Parlett recurrence, and judicious use of Padé approximants; the inclusion of new, unpublished research results and improved algorithms; a chapter devoted to the f(A)b problem; and a MATLAB® toolbox providing implementations of the key algorithms.Audience: This book is for specialists in numerical analysis and applied linear algebra as well as anyone wishing to learn about the theory of matrix functions and state of the art methods for computing them. It can be used for a graduate-level course on functions of matrices and is a suitable reference for an advanced course on applied or numerical linear algebra. It is also particularly well suited for self-study. Contents: List of Figures; List of Tables; Preface; Chapter 1: Theory of Matrix Functions; Chapter 2: Applications; Chapter 3: Conditioning; Chapter 4: Techniques for General Functions; Chapter 5: Matrix Sign Function; Chapter 6: Matrix Square Root; Chapter 7: Matrix pth Root; Chapter 8: The Polar Decomposition; Chapter 9: Schur-Parlett Algorithm; Chapter 10: Matrix Exponential; Chapter 11: Matrix Logarithm; Chapter 12: Matrix Cosine and Sine; Chapter 13: Function of Matrix Times Vector: f(A)b; Chapter 14: Miscellany; Appendix A: Notation; Appendix B: Background: Definitions and Useful Facts; Appendix C: Operation Counts; Appendix D: Matrix Function Toolbox; Appendix E: Solutions to Problems; Bibliography; Index.

Numerical Linear Algebra with Julia

Eric Darve,Mary Wootters
Numerical Linear Algebra with Julia Book PDF

Author : Eric Darve,Mary Wootters
Publisher : SIAM
Page : 420 pages
File Size : 50,5 Mb
Release : 2021-09-02
Category : Mathematics
ISBN : 9781611976557

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Numerical Linear Algebra with Julia by Eric Darve,Mary Wootters Pdf

Numerical Linear Algebra with Julia provides in-depth coverage of fundamental topics in numerical linear algebra, including how to solve dense and sparse linear systems, compute QR factorizations, compute the eigendecomposition of a matrix, and solve linear systems using iterative methods such as conjugate gradient. Julia code is provided to illustrate concepts and allow readers to explore methods on their own. Written in a friendly and approachable style, the book contains detailed descriptions of algorithms along with illustrations and graphics that emphasize core concepts and demonstrate the algorithms. Numerical Linear Algebra with Julia is a textbook for advanced undergraduate and graduate students in most STEM fields and is appropriate for courses in numerical linear algebra. It may also serve as a reference for researchers in various fields who depend on numerical solvers in linear algebra.

Numerical Linear Algebra

Folkmar Bornemann
Numerical Linear Algebra Book PDF

Author : Folkmar Bornemann
Publisher : Springer
Page : 153 pages
File Size : 50,8 Mb
Release : 2018-01-29
Category : Mathematics
ISBN : 9783319742229

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Numerical Linear Algebra by Folkmar Bornemann Pdf

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.

Numerical Linear Algebra with Applications

William Ford
Numerical Linear Algebra with Applications Book PDF

Author : William Ford
Publisher : Academic Press
Page : 629 pages
File Size : 49,6 Mb
Release : 2014-09-14
Category : Mathematics
ISBN : 9780123947840

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Numerical Linear Algebra with Applications by William Ford Pdf

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

Structured Matrices in Numerical Linear Algebra

Dario Andrea Bini,Fabio Di Benedetto,Eugene Tyrtyshnikov,Marc Van Barel
Structured Matrices in Numerical Linear Algebra Book PDF

Author : Dario Andrea Bini,Fabio Di Benedetto,Eugene Tyrtyshnikov,Marc Van Barel
Publisher : Springer
Page : 322 pages
File Size : 44,6 Mb
Release : 2019-04-08
Category : Mathematics
ISBN : 9783030040888

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Structured Matrices in Numerical Linear Algebra by Dario Andrea Bini,Fabio Di Benedetto,Eugene Tyrtyshnikov,Marc Van Barel Pdf

This book gathers selected contributions presented at the INdAM Meeting Structured Matrices in Numerical Linear Algebra: Analysis, Algorithms and Applications, held in Cortona, Italy on September 4-8, 2017. Highlights cutting-edge research on Structured Matrix Analysis, it covers theoretical issues, computational aspects, and applications alike. The contributions, written by authors from the foremost international groups in the community, trace the main research lines and treat the main problems of current interest in this field. The book offers a valuable resource for all scholars who are interested in this topic, including researchers, PhD students and post-docs.

An Introduction to Numerical Linear Algebra

Leslie Fox
An Introduction to Numerical Linear Algebra Book PDF

Author : Leslie Fox
Publisher : Oxford University Press, USA
Page : 354 pages
File Size : 53,7 Mb
Release : 1965
Category : Language Arts & Disciplines
ISBN : UOM:39015000962335

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An Introduction to Numerical Linear Algebra by Leslie Fox Pdf

Problems involving linear algebra arise in many contexts of scientific computation, either directly or through the replacement of continuous systems by discrete approximations. This introduction covers the practice of matrix algebra and manipulation, and the theory and practice of direct and iterative methods for solving linear simultaneous algebraic equations, inverting matrices, and determining the latent roots and vectors of matrices. Special attention is given to the important problem of error analysis and numerous examples illustrate the procedures recommended in various circumstances. The emphasis is on the reasons for selecting particular numerical methods rather than on programming or coding.

Applied Numerical Linear Algebra

William W. Hager
Applied Numerical Linear Algebra Book PDF

Author : William W. Hager
Publisher : SIAM
Page : 439 pages
File Size : 55,7 Mb
Release : 2022-01-21
Category : Mathematics
ISBN : 9781611976861

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Applied Numerical Linear Algebra by William W. Hager Pdf

This book introduces numerical issues that arise in linear algebra and its applications. It touches on a wide range of techniques, including direct and iterative methods, orthogonal factorizations, least squares, eigenproblems, and nonlinear equations. Detailed explanations on a wide range of topics from condition numbers to singular value decomposition are provided, as well as material on nonlinear and linear systems. Numerical examples, often based on discretizations of boundary-value problems, are used to illustrate concepts. Exercises with detailed solutions are provided at the end of the book, and supplementary material and updates are available online. This Classics edition is appropriate for junior and senior undergraduate students and beginning graduate students in courses such as advanced numerical analysis, special topics on numerical analysis, topics on data science, topics on numerical optimization, and topics on approximation theory.

Introduction to Numerical Linear Algebra and Optimisation

Philippe G. Ciarlet,Bernadette Miara,Jean-Marie Thomas
Introduction to Numerical Linear Algebra and Optimisation Book PDF

Author : Philippe G. Ciarlet,Bernadette Miara,Jean-Marie Thomas
Publisher : Cambridge University Press
Page : 456 pages
File Size : 45,9 Mb
Release : 1989-08-25
Category : Computers
ISBN : 0521339847

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Introduction to Numerical Linear Algebra and Optimisation by Philippe G. Ciarlet,Bernadette Miara,Jean-Marie Thomas Pdf

The purpose of this book is to give a thorough introduction to the most commonly used methods of numerical linear algebra and optimisation. The prerequisites are some familiarity with the basic properties of matrices, finite-dimensional vector spaces, advanced calculus, and some elementary notations from functional analysis. The book is in two parts. The first deals with numerical linear algebra (review of matrix theory, direct and iterative methods for solving linear systems, calculation of eigenvalues and eigenvectors) and the second, optimisation (general algorithms, linear and nonlinear programming). The author has based the book on courses taught for advanced undergraduate and beginning graduate students and the result is a well-organised and lucid exposition. Summaries of basic mathematics are provided, proofs of theorems are complete yet kept as simple as possible, and applications from physics and mechanics are discussed. Professor Ciarlet has also helpfully provided over 40 line diagrams, a great many applications, and a useful guide to further reading. This excellent textbook, which is translated and revised from the very successful French edition, will be of great value to students of numerical analysis, applied mathematics and engineering.