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Numerical Linear Algebra with Applications
Using MATLAB
A reference for students and professionals in engineering and science who need to compute solutions to solve practical problems
William Ford (Author)
9780123944351, Elsevier Science
Hardback, published 9 October 2014
628 pages
27.6 x 21.5 x 3.4 cm, 1.5 kg
"An important part of the book deals with iterative methods for solving large sparse systems. We can find here Jacobi, Gauss-Seidel and successive overrelaxation (SOR) methods, as well as Krylov subspace methods..." --Zentralblatt Math "...this is a book that merits careful consideration as a possible text for a course in numerical linear algebra, particularly one stressing applications to engineering and other areas of science." --MAA Reviews, January 2015
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.
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
Subject Areas: Programming & scripting languages: general [UMX], Numerical analysis [PBKS], Algebra [PBF]
