Matrices, Moments and Quadrature with Applications (eBook)

Gene H. Golub, Gerard Meurant (Autoren)

eBook Download: PDF

2009
376 Seiten
Princeton University Press (Verlag)
978-1-4008-3388-7 (ISBN)

Infos

This computationally oriented book describes and explains the mathematical relationships among matrices, moments, orthogonal polynomials, quadrature rules, and the Lanczos and conjugate gradient algorithms. The book bridges different mathematical areas to obtain algorithms to estimate bilinear forms involving two vectors and a function of the matrix. The first part of the book provides the necessary mathematical background and explains the theory. The second part describes the applications and gives numerical examples of the algorithms and techniques developed in the first part. Applications addressed in the book include computing elements of functions of matrices; obtaining estimates of the error norm in iterative methods for solving linear systems and computing parameters in least squares and total least squares; and solving ill-posed problems using Tikhonov regularization. This book will interest researchers in numerical linear algebra and matrix computations, as well as scientists and engineers working on problems involving computation of bilinear forms.

Autor

Gene H. Golub (1932-2007) was the Fletcher Jones Professor of Computer Science at Stanford University and the coauthor of Matrix Computations. Gérard Meurant, the author of three books on numerical linear algebra, has worked in scientific computing for almost four decades. He is retired from France's Commissariat à l'Énergie Atomique.

Produkt-Details

• Erscheint lt. Verlag: 7.12.2009
• Reihe/Serie: Princeton Series in Applied Mathematics
• Reihe/Serie: Princeton Series in Applied Mathematics
• Zusatzinfo: 88 line illus. 135 tables.
• Verlagsort: Princeton
• Sprache: englisch
• Themenwelt: Informatik ► Theorie / Studium ► Algorithmen
• Themenwelt: Mathematik / Informatik ► Mathematik ► Angewandte Mathematik
• Themenwelt: Technik
• Schlagworte: algorithm • analysis of algorithms • analytic function • asymptotic analysis • basis function • Basis (linear algebra) • Biconjugate gradient method • Bidiagonal matrix • bilinear form • Calculation • Characteristic Polynomial • Chebyshev Polynomials • coefficient • complex number • Computation • Condition number • Conjugate Gradient Method • Conjugate transpose • Cross-validation (statistics) • curve fitting • Degeneracy (mathematics) • Determinant • Diagonal matrix • Dimension (vector space) • Eigenvalues and Eigenvectors • Equation • estimation • Estimator • exponential function • Factorization • Functional Analysis • Function (mathematics) • Function of a real variable • Gaussian quadrature • Hankel matrix • Hermite interpolation • hessenberg matrix • Hilbert matrix • holomorphic function • Identity matrix • Interlacing (bitmaps) • Inverse iteration • inverse problem • Invertible matrix • Iteration • Iterative Method • Jacobi matrix • Krylov subspace • Laguerre polynomials • Lanczos algorithm • linear differential equation • linear regression • Linear subspace • logarithm • Machine epsilon • matrix function • Matrix polynomial • Maxima and minima • mean value theorem • Meromorphic Function • Moment (mathematics) • Moment matrix • Moment problem • monic polynomial • Monomial • Monotonic Function • Newton's method • Numerical analysis • Numerical Integration • numerical linear algebra • Orthogonal basis • orthogonality • orthogonalization • orthogonal matrix • orthogonal polynomials • Orthogonal transformation • Orthonormal basis • Partial fraction decomposition • polynomial • Preconditioner • QR algorithm • QR decomposition • quadratic form • Rate of Convergence • Recurrence relation • Regularization (mathematics) • Rotation Matrix • Singular value • Square (algebra) • Summation • Symmetric matrix • Theorem • Tikhonov regularization • Trace (linear algebra) • Triangular Matrix • tridiagonal matrix • Upper and lower bounds • Variable (mathematics) • Vector Space • Weight function
• ISBN-10: 1-4008-3388-4 / 1400833884
• ISBN-13: 978-1-4008-3388-7 / 9781400833887