Matrices, moments, and quadrature with applications [[electronic resource] /] / Gene H. Golub and Gerard Meurant

• Autore: Golub Gene H (Gene Howard), <1932-2007.>
• Pubblicazione: Princeton, N.J., : Princeton University Press, c2010
• Edizione: Course Book
• Descrizione fisica: 1 online resource (376 p.)
• Disciplina: 512.9434
• Soggetto topico: Matrices; Numerical analysis
• Soggetto non controllato: Algorithm; Analysis of algorithms; Analytic function; Asymptotic analysis; Basis (linear algebra); Basis function; 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; Function (mathematics); Function of a real variable; Functional analysis; 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; Orthogonal matrix; Orthogonal polynomials; Orthogonal transformation; Orthogonality; Orthogonalization; 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
• Classificazione: SK 915
• Altri autori: MeurantGérard A
• Note generali: Description based upon print version of record.
• Nota di bibliografia: Includes bibliographical references (p. 335-359) and index.
• Nota di contenuto: Frontmatter -- Contents -- Preface -- PART 1. Theory -- Chapter 1. Introduction -- Chapter 2. Orthogonal Polynomials -- Chapter 3. Properties of Tridiagonal Matrices -- Chapter 4. The Lanczos and Conjugate Gradient Algorithms -- Chapter 5. Computation of the Jacobi Matrices -- Chapter 6. Gauss Quadrature -- Chapter 7. Bounds for Bilinear Forms uTƒ(A)v -- Chapter 8. Extensions to Nonsymmetric Matrices -- Chapter 9. Solving Secular Equations -- PART 2. Applications -- Chapter 10. Examples of Gauss Quadrature Rules -- Chapter 11. Bounds and Estimates for Elements of Functions of Matrices -- Chapter 12. Estimates of Norms of Errors in the Conjugate Gradient Algorithm -- Chapter 13. Least Squares Problems -- Chapter 14. Total Least Squares -- Chapter 15. Discrete Ill-Posed Problems -- Bibliography -- Index
• Sommario/riassunto: 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.
• Titolo autorizzato: Matrices, moments and quadrature with applications
• ISBN: 1-282-45801-9; 1-282-93607-7; 9786612458019; 1-4008-3388-4
• Formato: Materiale a stampa
• Livello bibliografico: Monografia
• Lingua di pubblicazione: Inglese
• Record Nr.: 9910780861503321
• Lo trovi qui: Univ. Federico II
• Serie: Princeton series in applied mathematics.