Numerical Linear Algebra with Applications

Erscheinungsjahr 2014
ISBN: 978-0-12-394435-1
Verlag: ACADEMIC PRESS

Buch, Englisch, 628 Seiten, Format (B × H): 224 mm x 289 mm, Gewicht: 1786 g

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.

Zielgruppe

<p>Graduate or advanced undergraduate students in engineering, science, and mathematics, 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</p>

Autoren/Hrsg.

Ford, William

Fachgebiete

• Technische Wissenschaften Technik Allgemein Mathematik für Ingenieure
• Mathematik | Informatik Mathematik Numerik und Wissenschaftliches Rechnen Numerische Mathematik
• Mathematik | Informatik EDV | Informatik Informatik Mathematik für Informatiker
• Mathematik | Informatik Mathematik Mathematik Interdisziplinär Computeralgebra

Inhaltsverzeichnis

1. Matrices 2. Linear equations3. Subspaces4. Determinants5. Eigenvalues and eigenvectors6. Orthogonal vectors and matrices7. Vector and matrix norms8. Floating point arithmetic9. Algorithms10. Conditioning of problems and stability of algorithms11. Gaussian elimination and the LU decomposition12. Linear system applications13. Important special systems14. Gram-Schmidt decomposition15. The singular value decomposition16. Least-squares problems17. Implementing the QR factorization18. The algebraic eigenvalue problem19. The symmetric eigenvalue problem20. Basic iterative methods21. Krylov subspace methods22. Large sparse eigenvalue problems23. Computing the singular value decompositionAppendix A. Complex numbersAppendix B. Mathematical inductionAppendix C. Chebyshev polynomials

Über Autor(innen)

Ford, William
William Ford completed his undergraduate degree at MIT, having majored in mathematics and minored in electrical engineering. He went on to complete a Ph.D. in mathematics at the University of Illinois, Urbana-Champaign, with his thesis paper entitled "Numerical Solution of Pseudo-parabolic Partial Differential Equations," and after two years of researching and teaching within the Department of Mathematics at Clemson University he joined the faculty of the Mathematics Department at the University of the Pacific, in Stockton, California. Here he went on to become a founding member of the Department of the Computer Science. Beginning in the 1980s, he and William Topp began jointly publishing books, that included a Motorola 68000 assembly language book through D.C. Heath, a book on data structures with C++ through Prentice Hall, and a book on data structures with Java through Prentice Hall. Dr. Ford additionally developed an IDE (Integrated Development Environment) named "EZJava" to accompany the Java book and served as the Chair of the Computer Science Department until his retirement in 2014.