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Book
xxi, 756 p. : ill. ; 26 cm.
  • Matrix multiplication problems
  • Matrix analysis
  • General linear systems
  • Special linear systems
  • Orthogonalization and least squares
  • Parallel matrix computations
  • The unsymmetric eigenvalue problem
  • The symmetric eigenvalue problem
  • Lanczos methods
  • Iterative methods for linear systems
  • Functions of matrices
  • Special topics.
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 book to be an indispensible tool. 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; and, 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.
(source: Nielsen Book Data)9781421407944 20160615
Engineering Library (Terman)
CME-302-01
Book
xii, 217 p. : ill. ; 26 cm.
  • Preface-- 1. Introduction-- 2. Basic algorithms-- 3. Solving triangular systems-- 4. Cholesky factorization-- 5. Orthogonal methods-- 6. LU factorization-- 7. Fill-reducing orderings-- 8. Solving sparse linear systems-- 9. CSparse-- 10. Sparse matrices in MATLAB-- Appendix: Basics of the C programming language-- Bibliography-- Index.
  • (source: Nielsen Book Data)9780898716139 20160528
Computational scientists often encounter problems requiring the solution of sparse systems of linear equations. Attacking these problems efficiently requires an in-depth knowledge of the underlying theory, algorithms, and data structures found in sparse matrix software libraries. Here, Davis presents the fundamentals of sparse matrix algorithms to provide the requisite background. The book includes CSparse, a concise downloadable sparse matrix package that illustrates the algorithms and theorems presented in the book and equips readers with the tools necessary to understand larger and more complex software packages. With a strong emphasis on MATLAB(r) and the C programming language, Direct Methods for Sparse Linear Systems equips readers with the working knowledge required to use sparse solver packages and write code to interface applications to those packages. The book also explains how MATLAB performs its sparse matrix computations.
(source: Nielsen Book Data)9780898716139 20160528
Engineering Library (Terman), eReserve
CME-302-01
Book
xi, 419 p. : ill. (some col.) ; 26 cm.
  • Preface-- 1. Introduction-- 2. Linear equation solving-- 3. Linear least squares problems-- 4. Nonsymmetric Eigenvalue problems-- 5. The symmetric Eigenproblem and singular value decomposition-- 6. Iterative methods for linear systems-- 7. Iterative methods for Eigenvalue problems-- Bibliography-- Index.
  • (source: Nielsen Book Data)9780898713893 20160528
Designed for first-year graduate students from a variety of engineering and scientific disciplines, this comprehensive textbook covers the solution of linear systems, least squares problems, eigenvalue problems, and the singular value decomposition. The author, who helped design the widely used LAPACK and ScaLAPACK linear algebra libraries, draws on this experience to present state-of-the-art techniques for these problems, including recommending which algorithms to use in various practical situations. Algorithms are derived in a mathematically illuminating way, including condition numbers and error bounds. Direct and iterative algorithms, suitable for dense and sparse matrices, are discussed. Algorithm design for modern computer architectures, where moving data is often more expensive than arithmetic operations, is discussed in detail, using LAPACK as an illustration. There are many numerical examples throughout the text and in the problems at the ends of chapters, most of which are written in MATLAB and are freely available on the Web.
(source: Nielsen Book Data)9780898713893 20160528
Engineering Library (Terman), eReserve
CME-302-01
Book
xii, 361 p. : ill. ; 26 cm.
  • Preface-- Part I. Fundamental: 1. Matrix-vector multiplication-- 2. Orthogonal vectors and matrices-- 3. Norms-- 4. The singular value decomposition-- 5. More on the SVD-- Part II. QR Factorization and Least Squares: 6. Projectors-- 7. QR factorization-- 8. Gram-Schmidt orthogonalization-- 9. MATLAB-- 10. Householder triangularization-- 11. Least squares problems-- Part III. Conditioning and Stability: 12. Conditioning and condition numbers-- 13. Floating point arithmetic-- 14. Stability-- 15. More on stability-- 16. Stability of householder triangularization-- 17. Stability of back substitution-- 18. Conditioning of least squares problems-- 19. Stability of least squares algorithms-- Part IV. Systems of Equations: 20. Gaussian elimination-- 21. Pivoting-- 22. Stability of Gaussian elimination-- 23. Cholesky factorization-- Part V. Eigenvalues: 24. Eigenvalue problems-- 25. Overview of Eigenvalue algorithms-- 26. Reduction to Hessenberg or tridiagonal form-- 27. Rayleigh quotient, inverse iteration-- 28. QR algorithm without shifts-- 29. QR algorithm with shifts-- 30. Other Eigenvalue algorithms-- 31. Computing the SVD-- Part VI. Iterative Methods: 32. Overview of iterative methods-- 33. The Arnoldi iteration-- 34. How Arnoldi locates Eigenvalues-- 35. GMRES-- 36. The Lanczos iteration-- 37. From Lanczos to Gauss quadrature-- 38. Conjugate gradients-- 39. Biorthogonalization methods-- 40. Preconditioning-- Appendix-- Notes-- Bibliography-- Index.
  • (source: Nielsen Book Data)9780898713619 20160528
This is a concise, insightful introduction to the field of numerical linear algebra. The clarity and eloquence of the presentation make it popular with teachers and students alike. The text aims to expand the reader's view of the field and to present standard material in a novel way. All of the most important topics in the field are covered with a fresh perspective, including iterative methods for systems of equations and eigenvalue problems and the underlying principles of conditioning and stability. Presentation is in the form of 40 lectures, which each focus on one or two central ideas. The unity between topics is emphasized throughout, with no risk of getting lost in details and technicalities. The book breaks with tradition by beginning with the QR factorization - an important and fresh idea for students, and the thread that connects most of the algorithms of numerical linear algebra.
(source: Nielsen Book Data)9780898713619 20160528
Engineering Library (Terman)
CME-302-01