Matrix Functions And Matrix Equations

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Matrix Functions And Matrix Equations

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Author : Zhaojun Bai
language : en
Publisher: World Scientific
Release Date : 2015-09-04

Matrix Functions And Matrix Equations written by Zhaojun Bai and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-09-04 with Mathematics categories.

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.

Matrices And Calculus

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Author : Dr. Renuka Devi K
language : en
Publisher: RK Publication
Release Date : 2024-08-01

Matrices And Calculus written by Dr. Renuka Devi K and has been published by RK Publication this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-08-01 with Mathematics categories.

Matrices and Calculus the foundations and applications of matrix theory and calculus, offering readers a blend of theoretical insights and practical problem-solving techniques. Ideal for students and professionals alike, this book covers essential topics such as matrix operations, determinants, eigenvalues, derivatives, and integrals. Advanced applications in engineering, physics, and computer science, making complex concepts accessible through clear explanations, illustrative examples, and exercises. Whether used as a textbook or a reference, *Matrices and Calculus* provides the tools needed to navigate these critical areas of mathematics with confidence.

Functions Of Matrices

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Author : Nicholas J. Higham
language : en
Publisher: SIAM
Release Date : 2008-09-11

Functions Of Matrices written by Nicholas J. Higham and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008-09-11 with Mathematics categories.

“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.

Linear Algebra And Matrix Computations With Matlab

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Author : Dingyü Xue
language : en
Publisher: Walter de Gruyter GmbH & Co KG
Release Date : 2020-03-23

Linear Algebra And Matrix Computations With Matlab written by Dingyü Xue and has been published by Walter de Gruyter GmbH & Co KG this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-03-23 with Computers categories.

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.

Matrix Functions Defined By Differential Equations

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Author : John Orin Mayhugh
language : en
Publisher:
Release Date : 1936

Matrix Functions Defined By Differential Equations written by John Orin Mayhugh and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1936 with Functions categories.

Matrices

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Author : Pam Norton
language : en
Publisher: Aust Council for Ed Research
Release Date : 2007

Matrices written by Pam Norton and has been published by Aust Council for Ed Research this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007 with Education categories.

This book provides mathematics teachers with an elementary introduction to matrix algebra and its uses in formulating and solving practical problems, solving systems of linear equations, representing combinations of affine (including linear) transformations of the plane and modelling finite state Markov chains.

Hierarchical Matrices Algorithms And Analysis

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Author : Wolfgang Hackbusch
language : en
Publisher: Springer
Release Date : 2015-12-21

Hierarchical Matrices Algorithms And Analysis written by Wolfgang Hackbusch and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-12-21 with Mathematics categories.

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.

The Theory Of Matrices

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Author : Peter Lancaster
language : en
Publisher: Academic Press
Release Date : 1985-05-28

The Theory Of Matrices written by Peter Lancaster and has been published by Academic Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1985-05-28 with Computers categories.

Matrix algebra; Determinants, inverse matrices, and rank; Linear, euclidean, and unitary spaces; Linear transformations and matrices; Linear transformations in unitary spaces and simple matrices; The jordan canonical form: a geometric approach; Matrix polynomials and normal forms; The variational method; Functions of matrices; Norms and bounds for eigenvalues; Perturbation theory; Linear matrices equations and generalized inverses; Stability problems; Matrix polynomials; Nonnegative matrices.

The Collected Mathematical Papers Of Arthur Cayley

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Author : Arthur Cayley
language : en
Publisher:
Release Date : 1889

The Collected Mathematical Papers Of Arthur Cayley written by Arthur Cayley and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1889 with Mathematics categories.

The Mathematics Of Matrices

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Author : Philip J. Davis
language : en
Publisher:
Release Date : 1965

The Mathematics Of Matrices written by Philip J. Davis and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1965 with Matrices categories.