numerical methods in matrix computations texts in applied mathematics

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Numerical Methods In Matrix Computations

Author : Åke Björck
ISBN : 9783319050898
Genre : Mathematics
File Size : 85. 69 MB
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Matrix algorithms are at the core of scientific computing and are indispensable tools in most applications in engineering. This book offers a comprehensive and up-to-date treatment of modern methods in matrix computation. It uses a unified approach to direct and iterative methods for linear systems, least squares and eigenvalue problems. A thorough analysis of the stability, accuracy, and complexity of the treated methods is given. Numerical Methods in Matrix Computations is suitable for use in courses on scientific computing and applied technical areas at advanced undergraduate and graduate level. A large bibliography is provided, which includes both historical and review papers as well as recent research papers. This makes the book useful also as a reference and guide to further study and research work.

Handbook For Matrix Computations

Author : Thomas F. Coleman
ISBN : 0898712270
Genre : Mathematics
File Size : 78. 42 MB
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Mathematics of Computing -- Numerical Analysis.

Numerical Mathematics

Author : Alfio Maria Quarteroni
ISBN : 9780387227504
Genre : Mathematics
File Size : 72. 20 MB
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The purpose of this book is to provide the mathematical foundations of numerical methods, to analyze their basic theoretical properties and to demonstrate their performances on examples and counterexamples. Within any specific class of problems, the most appropriate scientific computing algorithms are reviewed, their theoretical analyses are carried out and the expected results are verified using the MATLAB software environment. Each chapter contains examples, exercises and applications of the theory discussed to the solution of real-life problems. While addressed to senior undergraduates and graduates in engineering, mathematics, physics and computer sciences, this text is also valuable for researchers and users of scientific computing in a large variety of professional fields.

Applied Numerical Linear Algebra

Author : James W. Demmel
ISBN : 9780898713893
Genre : Mathematics
File Size : 32. 78 MB
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This comprehensive textbook is designed for first-year graduate students from a variety of engineering and scientific disciplines.

Functions Of Matrices

Author : Nicholas J. Higham
ISBN : 9780898717778
Genre : Factorization (Mathematics)
File Size : 70. 5 MB
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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.

Accuracy And Stability Of Numerical Algorithms

Author : Nicholas J. Higham
ISBN : 0898718023
Genre : Computer algorithms
File Size : 66. 19 MB
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Accuracy and Stability of Numerical Algorithms gives a thorough, up-to-date treatment of the behavior of numerical algorithms in finite precision arithmetic. It combines algorithmic derivations, perturbation theory, and rounding error analysis, all enlivened by historical perspective and informative quotations. This second edition expands and updates the coverage of the first edition (1996) and includes numerous improvements to the original material. Two new chapters treat symmetric indefinite systems and skew-symmetric systems, and nonlinear systems and Newton's method. Twelve new sections include coverage of additional error bounds for Gaussian elimination, rank revealing LU factorizations, weighted and constrained least squares problems, and the fused multiply-add operation found on some modern computer architectures.

Numerical Methods For Large Eigenvalue Problems

Author : Yousef Saad
ISBN : 1611970733
Genre : Eigenvalues
File Size : 42. 51 MB
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This revised edition discusses numerical methods for computing eigenvalues and eigenvectors of large sparse matrices. It provides an in-depth view of the numerical methods that are applicable for solving matrix eigenvalue problems that arise in various engineering and scientific applications. Each chapter was updated by shortening or deleting outdated topics, adding topics of more recent interest, and adapting the Notes and References section. Significant changes have been made to Chapters 6 through 8, which describe algorithms and their implementations and now include topics such as the implicit restart techniques, the Jacobi-Davidson method, and automatic multilevel substructuring.

Numerical Methods In Scientific Computing

Author : Germund Dahlquist
ISBN : 9780898716443
Genre : Mathematics
File Size : 27. 91 MB
Format : PDF
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This work addresses the increasingly important role of numerical methods in science and engineering. It combines traditional and well-developed topics with other material such as interval arithmetic, elementary functions, operator series, convergence acceleration, and continued fractions.

Applied Linear Algebra And Matrix Analysis

Author : Thomas S. Shores
ISBN : 9783319747484
Genre : Mathematics
File Size : 32. 53 MB
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This new book offers a fresh approach to matrix and linear algebra by providing a balanced blend of applications, theory, and computation, while highlighting their interdependence. Intended for a one-semester course, Applied Linear Algebra and Matrix Analysis places special emphasis on linear algebra as an experimental science, with numerous examples, computer exercises, and projects. While the flavor is heavily computational and experimental, the text is independent of specific hardware or software platforms. Throughout the book, significant motivating examples are woven into the text, and each section ends with a set of exercises.

Matrix Computations

Author : Gene H. Golub
ISBN : 9781421408590
Genre : Mathematics
File Size : 21. 40 MB
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The fourth edition of Gene H. Golub and Charles F. Van Loan's classic is an essential reference for computational scientists and engineers in addition to researchers in the numerical linear algebra community. Anyone whose work requires the solution to a matrix problem and an appreciation of its mathematical properties will find this text useful and engaging. This revision is a cover-to-cover expansion and renovation of the third edition. It now includes an introduction to tensor computations and brand new sections on • fast transforms• parallel LU• discrete Poisson solvers• pseudospectra• structured linear equation problems• structured eigenvalue problems• large-scale SVD methods• polynomial eigenvalue problems Matrix Computations is packed with challenging problems, insightful derivations, and pointers to the literature—everything needed to become a matrix-savvy developer of numerical methods and software.

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