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Author: Zhaojun Bai
Publisher: World Scientific
ISBN: 9814675784
Category : Mathematics
Languages : en
Pages : 148
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Book Description
Matrix functions and matrix equations are widely used in science, engineering and social sciences due to the succinct and insightful way in which they allow problems to be formulated and solutions to be expressed. This book covers materials relevant to advanced undergraduate and graduate courses in numerical linear algebra and scientific computing. It is also well-suited for self-study. The broad content makes it convenient as a general reference to the subjects. Contents:Matrix Functions: A Short Course (Nicholas J Higham and Lijing Lin)A Short Course on Exponential Integrators (Marlis Hochbruck)Matrix Equations and Model Reduction (Peter Benner, Tobias Breiten and Lihong Feng)Rayleigh Quotient Based Optimization Methods for Eigenvalue Problems (Ren-Cang Li)Factorization-Based Sparse Solvers and Preconditioners (Xiaoye Sherry Li) Readership: Researchers and graduate students in numerical and computational mathematics. Key Features:The book covers underlying theory and a variety of algorithms for matrix functions and matrix equations. The book also covers high performance linear system solvers and eigenvalue computations which are computational kernels to matrix functions and matrix equationsThe book provides the current developments and applications beyond the material found in regular university courses and textbooks. It includes a comprehensive list of latest referencesThe authors of the chapters are leading experts who are also well-known for their expository skillsKeywords:Matrix Functions;Matrix Equations;Numerical Linear Algebra;Exponential Integral
Author: Zhaojun Bai
Publisher: World Scientific
ISBN: 9814675784
Category : Mathematics
Languages : en
Pages : 148
Get Book
Book Description
Matrix functions and matrix equations are widely used in science, engineering and social sciences due to the succinct and insightful way in which they allow problems to be formulated and solutions to be expressed. This book covers materials relevant to advanced undergraduate and graduate courses in numerical linear algebra and scientific computing. It is also well-suited for self-study. The broad content makes it convenient as a general reference to the subjects. Contents:Matrix Functions: A Short Course (Nicholas J Higham and Lijing Lin)A Short Course on Exponential Integrators (Marlis Hochbruck)Matrix Equations and Model Reduction (Peter Benner, Tobias Breiten and Lihong Feng)Rayleigh Quotient Based Optimization Methods for Eigenvalue Problems (Ren-Cang Li)Factorization-Based Sparse Solvers and Preconditioners (Xiaoye Sherry Li) Readership: Researchers and graduate students in numerical and computational mathematics. Key Features:The book covers underlying theory and a variety of algorithms for matrix functions and matrix equations. The book also covers high performance linear system solvers and eigenvalue computations which are computational kernels to matrix functions and matrix equationsThe book provides the current developments and applications beyond the material found in regular university courses and textbooks. It includes a comprehensive list of latest referencesThe authors of the chapters are leading experts who are also well-known for their expository skillsKeywords:Matrix Functions;Matrix Equations;Numerical Linear Algebra;Exponential Integral
Author: Nicholas J. Higham
Publisher: SIAM
ISBN: 0898717779
Category : Mathematics
Languages : en
Pages : 445
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Book Description
A thorough and elegant treatment of the theory of matrix functions and numerical methods for computing them, including an overview of applications, new and unpublished research results, and improved algorithms. Key features include a detailed treatment of the matrix sign function and matrix roots; a development of the theory of conditioning and properties of the Fre;chet derivative; Schur decomposition; block Parlett recurrence; a thorough analysis of the accuracy, stability, and computational cost of numerical methods; general results on convergence and stability of matrix iterations; and a chapter devoted to the f(A)b problem. Ideal for advanced courses and for self-study, its broad content, references and appendix also make this book a convenient general reference. Contains an extensive collection of problems with solutions and MATLAB implementations of key algorithms.
Author: Dingyü Xue
Publisher: Walter de Gruyter GmbH & Co KG
ISBN: 3110666995
Category : Computers
Languages : en
Pages : 301
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Book Description
This book focuses the solutions of linear algebra and matrix analysis problems, with the exclusive use of MATLAB. The topics include representations, fundamental analysis, transformations of matrices, matrix equation solutions as well as matrix functions. Attempts on matrix and linear algebra applications are also explored.
Author: Stephen Boyd
Publisher: Cambridge University Press
ISBN: 1316518965
Category : Business & Economics
Languages : en
Pages : 477
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Book Description
A groundbreaking introduction to vectors, matrices, and least squares for engineering applications, offering a wealth of practical examples.
Author: Wilhelmus H. Schilders
Publisher: Springer Science & Business Media
ISBN: 3540788417
Category : Mathematics
Languages : en
Pages : 471
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Book Description
The idea for this book originated during the workshop “Model order reduction, coupled problems and optimization” held at the Lorentz Center in Leiden from S- tember 19–23, 2005. During one of the discussion sessions, it became clear that a book describing the state of the art in model order reduction, starting from the very basics and containing an overview of all relevant techniques, would be of great use for students, young researchers starting in the ?eld, and experienced researchers. The observation that most of the theory on model order reduction is scattered over many good papers, making it dif?cult to ?nd a good starting point, was supported by most of the participants. Moreover, most of the speakers at the workshop were willing to contribute to the book that is now in front of you. The goal of this book, as de?ned during the discussion sessions at the workshop, is three-fold: ?rst, it should describe the basics of model order reduction. Second, both general and more specialized model order reduction techniques for linear and nonlinear systems should be covered, including the use of several related numerical techniques. Third, the use of model order reduction techniques in practical appli- tions and current research aspects should be discussed. We have organized the book according to these goals. In Part I, the rationale behind model order reduction is explained, and an overview of the most common methods is described.
Author: Lynn Marecek
Publisher:
ISBN: 9781951693848
Category :
Languages : en
Pages :
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Book Description
Author: Richard Bronson
Publisher: Academic Press
ISBN: 1483216616
Category : Mathematics
Languages : en
Pages : 300
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Book Description
Matrix Methods: An Introduction is a nine-chapter text that emphasizes the methodological aspects of mathematical matrices. This book is intended for an introductory course in matrices similar to those given to sophomore and junior engineering students at Fairleigh Dickinson University. The first five chapters deal with the elementary aspects of matrices, including their definition, determinants, method of inversion, simultaneous linear equations, eigenvalues, and eigenvectors. The remaining chapters explore the materials of fundamental importance to both engineers and scientists. These chapters discuss the principles of matrix calculus, linear differential equations, Jordan canonical forms, and special matrices. A set of exercises is provided at the end of each section, which is basically routine in nature and serves primarily to enhance the reader's ability to use the methods just presented. On occasion, problems are assigned that will extend or complete topics previously introduced. This book is intended primarily for science, engineering, and applied mathematics students.
Author: Robert R. Stoll
Publisher: Courier Corporation
ISBN: 0486623181
Category : Mathematics
Languages : en
Pages : 290
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Book Description
Advanced undergraduate and first-year graduate students have long regarded this text as one of the best available works on matrix theory in the context of modern algebra. Teachers and students will find it particularly suited to bridging the gap between ordinary undergraduate mathematics and completely abstract mathematics. The first five chapters treat topics important to economics, psychology, statistics, physics, and mathematics. Subjects include equivalence relations for matrixes, postulational approaches to determinants, and bilinear, quadratic, and Hermitian forms in their natural settings. The final chapters apply chiefly to students of engineering, physics, and advanced mathematics. They explore groups and rings, canonical forms for matrixes with respect to similarity via representations of linear transformations, and unitary and Euclidean vector spaces. Numerous examples appear throughout the text.
Author: Zhaojun Bai
Publisher: World Scientific
ISBN: 9814675776
Category : Mathematics
Languages : en
Pages : 146
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Book Description
"Matrix functions and matrix equations are widely used in science, engineering and social sciences due to the succinct and insightful way in which they allow problems to be formulated and solutions to be expressed. This book covers materials relevant to advanced undergraduate and graduate courses in numerical linear algebra and scientific computing. It is also well-suited for self-study. The broad content makes it convenient as a general reference to the subjects."--
Author: Jay Abramson
Publisher:
ISBN: 9789888407439
Category : Mathematics
Languages : en
Pages : 892
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Book Description
College Algebra provides a comprehensive exploration of algebraic principles and meets scope and sequence requirements for a typical introductory algebra course. The modular approach and richness of content ensure that the book meets the needs of a variety of courses. College Algebra offers a wealth of examples with detailed, conceptual explanations, building a strong foundation in the material before asking students to apply what they've learned. Coverage and Scope In determining the concepts, skills, and topics to cover, we engaged dozens of highly experienced instructors with a range of student audiences. The resulting scope and sequence proceeds logically while allowing for a significant amount of flexibility in instruction. Chapters 1 and 2 provide both a review and foundation for study of Functions that begins in Chapter 3. The authors recognize that while some institutions may find this material a prerequisite, other institutions have told us that they have a cohort that need the prerequisite skills built into the course. Chapter 1: Prerequisites Chapter 2: Equations and Inequalities Chapters 3-6: The Algebraic Functions Chapter 3: Functions Chapter 4: Linear Functions Chapter 5: Polynomial and Rational Functions Chapter 6: Exponential and Logarithm Functions Chapters 7-9: Further Study in College Algebra Chapter 7: Systems of Equations and Inequalities Chapter 8: Analytic Geometry Chapter 9: Sequences, Probability and Counting Theory
