Author | Samarskii, Aleksandr A. author |
---|---|

Title | Numerical Methods for Grid Equations [electronic resource] : Volume II Iterative Methods / by Aleksandr A. Samarskii, Evgenii S. Nikolaev |

Imprint | Basel : Birkhรคuser Basel, 1989 |

Connect to | http://dx.doi.org/10.1007/978-3-0348-9142-4 |

Descript | XVI, 502 p. online resource |

CONTENT

5 The Mathematical Theory of Iterative Methods -- 5.1 Several results from functional analysis -- 5.2 Difference schemes as operator equations -- 5.3 Basic concepts from the theory of iterative methods -- 6 Two-Level Iterative Methods -- 6.1 Choosing the iterative parameters -- 6.2 The Chebyshev two-level method -- 6.3 The simple iteration method -- 6.4 The non-self-adjoint case. The simple iteration method -- 6.5 Sample applications of the iterative methods -- 7 Three-Level Iterative Methods -- 7.1 An estimate of the convergence rate -- 7.2 The Chebyshev semi-iterative method -- 7.3 The stationary three-level method -- 7.4 The stability of two-level and three-level methods relative to a priori data -- 8 Iterative Methods of Variational Type -- 8.1 Two-level gradient methods -- 8.2 Examples of two-level gradient methods -- 8.3 Three-level conjugate-direction methods -- 8.4 Examples of the three-level methods -- 8.5 Accelerating the convergence of two-level methods in the self-adjoint case -- 9 Triangular Iterative Methods -- 9.1 The Gauss-Seidel method -- 9.2 The successive over-relaxation method -- 9.3 Triangular methods -- 10 The Alternate-Triangular Method -- 10.1 The general theory of the method -- 10.2 Boundary-value difference problems for elliptic equations in a rectangle -- 10.3 The alternate-triangular method for elliptic equations in arbitrary regions -- 11 The Alternating-Directions Method -- 11.1 The alternating-directions method in the commutative case -- 11.2 Sample applications of the method -- 11.3 The alternating-directions method in the general case -- 12 Methods for Solving Equationswith Indefinite and Singular Operators -- 12.1 Equations with real indefinite operators -- 12.2 Equations with complex operators -- 12.3 General iterative methods for equations with singular operators -- 12.4 Special methods -- 13 Iterative Methods for Solving Non-Linear Equations -- 13.1 Iterative methods. The general theory -- 13.2 Methods for solving non-linear difference schemes -- 14 Example Solutions of Elliptic Grid Equations -- 14.1 Methods for constructing implicit iterative schemes -- 14.3 Systems of elliptic equations -- 14.4 Methods for solving elliptic equations in irregular regions -- 15 Methods for Solving Elliptic Equationsin Curvilinear Orthogonal Coordinates -- 15.1 Posing boundary-value problems for differential equations -- 15.2 The solution of difference problems in cylindrical coordinates -- 15.3 Solution of difference problems in polar coordinate systems -- Appendices -- Construction of the minimax polynomial -- Translatorโ{128}{153}s note

Mathematics
Computer mathematics
Mathematics
Computational Mathematics and Numerical Analysis