Matrix Computations (Johns Hopkins Studies in the Mathematical Sciences)

Matrix Computations is a landmark book in the literature on the computer sciences: informative. up-to-date, and above all, practical. For use in the classroom and the research library, it provides the vital mathematical background and algorithmic skills required in the production of numerical software. Gene Golub and Charles Van Loan combine the uncluttered presentation and problem-solving opportunities of a fine textbook with the detailed bibliographies and strong algorithmic content required by professional readers. While discussing such general principles as the exploitation of structure , reliance on orthogonal transformations, and the assessment of problem sensitivity, the authors touch on numerous specifics, including Toeplitz systems, Vandermonde systems, constrained least squares, generalized eigenvalue problems, and matrix function problems. No other book covers the field of linear algebra as completely as Matrix Computations. Of particular interest are the authors' discussions in depth of singular value decomposition and its varied applications, the pedagogic derivation of the QR algorithm, and a survey of Lanczos and conjugate gradient techniques. Students, computer scientists, computer engineers, and mathematicians in numerical analysis will all use this book as a reference.