Author | Kress, Rainer. author |
---|---|
Title | Numerical Analysis [electronic resource] / by Rainer Kress |
Imprint | New York, NY : Springer New York : Imprint: Springer, 1998 |
Connect to | http://dx.doi.org/10.1007/978-1-4612-0599-9 |
Descript | XII, 326 p. online resource |
1 Introduction -- 2 Linear Systems -- 2.1 Examples for Systems of Equations -- 2.2 Gaussian Elimination -- 2.3 LR Decomposition -- 2.4 QR Decomposition -- Problems -- 3 Basic Functional Analysis -- 3.1 Normed Spaces -- 3.2 Scalar Products -- 3.3 Bounded Linear Operators -- 3.4 Matrix Norms -- 3.5 Completeness -- 3.6 The Banach Fixed Point Theorem -- 3.7 Best Approximation -- Problems -- 4 Iterative Methods for Linear Systems -- 4.1 Jacobi and GaussโSeidel Iterations -- 4.2 Relaxation Methods -- 4.3 Two-Grid Methods -- Problems -- 5 Ill-Conditioned Linear Systems -- 5.1 Condition Number -- 5.2 Singular Value Decomposition -- 5.3 Tikhonov Regularization -- Problems -- 6 Iterative Methods for Nonlinear Systems -- 6.1 Successive Approximations -- 6.2 Newtonโs Method -- 6.3 Zeros of Polynomials -- 6.4 Least Squares Problems -- Problems -- 7 Matrix Eigenvalue Problems -- 7.1 Examples -- 7.2 Estimates for the Eigenvalues -- 7.3 The Jacobi Method -- 7.4 The QR Algorithm -- 7.5 Hessenberg Matrices -- Problems -- 8 Interpolation -- 8.1 Polynomial Interpolation -- 8.2 Trigonometric Interpolation -- 8.3 Spline Interpolation -- 8.4 Bรฉzier Polynomials -- Problems -- 9 Numerical Integration -- 9.1 Interpolatory Quadratures -- 9.2 Convergence of Quadrature Formulae -- 9.3 Gaussian Quadrature Formulae -- 9.4 Quadrature of Periodic Functions -- 9.5 Romberg Integration -- 9.6 Improper Integrals -- Problems -- 10 Initial Value Problems -- 10.1 The PicardโLindelรถf Theorem -- 10.2 Eulerโs Method -- 10.3 Single-Step Methods -- 10.4 Multistep Methods -- Problems -- 11 Boundary Value Problems -- 11.1 Shooting Methods -- 11.2 Finite Difference Methods -- 11.3 The Riesz and Lax-Milgram Theorems -- 11.4 Weak Solutions -- 11.5 The Finite Element Method -- Problems -- 12 Integral Equations -- 12.1 The Riesz Theory -- 12.2 Operator Approximations -- 12.3 Nystrรถmโs Method -- 12.4 The Collocation Method -- 12.5 Stability -- Problems -- References