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allaire g kaber s numerical linear algebra 2007

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Textbook in PDF format This book brings together linear algebra, numerical methods and an easy to use programming environment under Matlab (or Scilab). One of the key features of the book are the worked out examples and exercises at the end of each chapter. The reader is asked to do some numerical experiments in Matlab and then to prove the results theoretically. The book is a combination and update of two earlier French books by the authors. It is appropriate for both undergraduate and beginning graduate courses in mathematics as well as for working scientists and engineers as a self-study tool and reference. This book is about numerical linear algebra and focuses on practical algorithms for solving computer problems of linear algebra. Discretization of a Differential Equation Least Squares Fitting Vibrations of a Mechanical System The Vibrating String Image Compression by the SVD Factorization Definition and Properties of Matrices Gram–Schmidt Orthonormalization Process Matrices Spectral Theory of Matrices Matrix Triangularization Matrix Diagonalization Min–Max Principle Singular Values of a Matrix Matrix Norms, Sequences, and Series Matrix Norms and Subordinate Norms Subordinate Norms for Rectangular Matrices Matrix Sequences and Series Introduction to Algorithmics Algorithms and pseudolanguage Operation Count and Complexity The Strassen Algorithm Equivalence of Operations LinearSystems Square Linear Systems Over- and Underdetermined Linear Systems Numerical Solution Direct Methods for Linear Systems Gaussian Elimination Method LU Decomposition Method Cholesky Method QR Factorization Method Least Squares Problems Motivation Main Results Numerical Algorithms Simple Iterative Methods General Setting Jacobi, Gauss–Seidel, and Relaxation Methods The Special Case of Tridiagonal Matrices Discrete Laplacian Programming Iterative Methods Block Methods Conjugate Gradient Method The Gradient Method Geometric Interpretation Some Ideas for Further Generalizations Theoretical Definition of the Conjugate Gradient Method Conjugate Gradient Algorithm Methods for Computing Eigenvalues Generalities Conditioning Power Method Jacobi Method Givens–Householder Method QR Method Lanczos Method Solutions and Programs Index of Programs

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allaire g kaber s numerical linear algebra 2007