Gurantor department | Department of Applied Mathematics | Credits | 6 |

Subject guarantor | Ing. Simona Bérešová, Ph.D. | Subject version guarantor | Ing. Simona Bérešová, Ph.D. |

Study level | undergraduate or graduate | Requirement | Choice-compulsory type B |

Year | Semester | winter | |

Study language | Czech | ||

Year of introduction | 2019/2020 | Year of cancellation | |

Intended for the faculties | FEI | Intended for study types | Follow-up Master |

Instruction secured by | |||
---|---|---|---|

Login | Name | Tuitor | Teacher giving lectures |

DOM0015 | Ing. Simona Bérešová, Ph.D. |

Extent of instruction for forms of study | ||
---|---|---|

Form of study | Way of compl. | Extent |

Full-time | Credit and Examination | 2+2 |

Part-time | Credit and Examination | 10+10 |

Students will be able to use various types of iterative methods for solving linear and nonlinear alebraic systems. He will become acquainted with basic ideas as well as some recent results in the field.

Lectures

Tutorials

The course introduces various types of iterative methods for solving linear
and nonlinear systems. The lectures focus on the basic ideas, however, it include some latest results in the field.

C.T. Kelley, Iterative Methods for Linear and Nonlinear Equations, SIAM,
Philadelphia 1995, http://www.siam.org/catalog/mcc12/kelley.htm
B. Barrett et al.: Templates for the solution of linear systems, SIAM,
Philadelphia 1993, http://www.siam.org/catalog/mcc01/barrett.htm

O. Axelsson: Iterative Solution Methods, Cambridge University Press, 1994
Werner C. Rheinboldt: Methods for Solving Systems of Nonlinear Equations,
SIAM, Philadelphia 1998, http://www.siam.org/catalog/mcc02/cb70.htm

Obhajoba semestrálního projektu.
Zkouška písemná a ústní.

There are not defined other requirements for student.

Subject has no prerequisities.

Subject has no co-requisities.

Lectures:
Systems of equations arising from mathematical modelling in engineering.
Properties of systems arising from finite element methods.
Classical iterative methods. Richardson, Jacobi, Gauss-Seidel iterative methods. Convergence studies.
Multigrid methods.
Method of conjugate gradients. Fundamentals. Implementation.
Global properties and convergence rate estimates based on the condition number.
Preconditioning. Preconditioned conjugate gradients method. Incomplete factorization.
Solution to nonsymmetric systems. GMRES.
Solution to nonlinear systems. Properties of nonlinear operators. Newton method. Local convergence. Inexact Newton method. Damping and global convergence.
Implementation of iterative methods on parallel computers. Domain decomposition methods.
Comparison of direct and iterative methods. Solution to large-scale systems.
Tutorials:
Systems of equations arising in mathematical modeling in engineering. Assembling the system matrix in the finite element method, properties.
Solution to systems using Richardson, Jacobi, and Gauss-Seidel iterative methods. Multigrid method.
Implementation of conjugate gradient method, rate of convergence.
Implementation of various preconditioners in the conjugate gradients method. Incomplete factorization.
Implementation of GMRES.
Implementation of Newton method and inexact Newton method.
Implementation of iterative methods on parallel computers. Domain decomposition methods.
Comparison of direct and iterative methods. Solution to large-scale systems.

Task name | Type of task | Max. number of points
(act. for subtasks) | Min. number of points | Max. počet pokusů |
---|---|---|---|---|

Credit and Examination | Credit and Examination | 100 (100) | 51 | |

Credit | Credit | 30 | 15 | |

Examination | Examination | 70 | 36 | 3 |

Show history

Conditions for subject completion and attendance at the exercises within ISP: Completion of all mandatory tasks within individually agreed deadlines

Show history

Academic year | Programme | Branch/spec. | Spec. | Zaměření | Form | Study language | Tut. centre | Year | W | S | Type of duty | |
---|---|---|---|---|---|---|---|---|---|---|---|---|

2024/2025 | (N0541A170007) Computational and Applied Mathematics | (S01) Applied Mathematics | K | Czech | Ostrava | Choice-compulsory type B | study plan | |||||

2024/2025 | (N0541A170007) Computational and Applied Mathematics | (S01) Applied Mathematics | P | Czech | Ostrava | Choice-compulsory type B | study plan | |||||

2023/2024 | (N0541A170007) Computational and Applied Mathematics | (S01) Applied Mathematics | P | Czech | Ostrava | Choice-compulsory type B | study plan | |||||

2023/2024 | (N0541A170007) Computational and Applied Mathematics | (S01) Applied Mathematics | K | Czech | Ostrava | Choice-compulsory type B | study plan | |||||

2022/2023 | (N0541A170007) Computational and Applied Mathematics | (S01) Applied Mathematics | K | Czech | Ostrava | Choice-compulsory type B | study plan | |||||

2022/2023 | (N0541A170007) Computational and Applied Mathematics | (S01) Applied Mathematics | P | Czech | Ostrava | Choice-compulsory type B | study plan | |||||

2021/2022 | (N0541A170007) Computational and Applied Mathematics | (S01) Applied Mathematics | P | Czech | Ostrava | Choice-compulsory type B | study plan | |||||

2021/2022 | (N0541A170007) Computational and Applied Mathematics | (S01) Applied Mathematics | K | Czech | Ostrava | Choice-compulsory type B | study plan | |||||

2020/2021 | (N0541A170007) Computational and Applied Mathematics | (S01) Applied Mathematics | K | Czech | Ostrava | Choice-compulsory type B | study plan | |||||

2020/2021 | (N0541A170007) Computational and Applied Mathematics | (S01) Applied Mathematics | P | Czech | Ostrava | Choice-compulsory type B | study plan | |||||

2019/2020 | (N0541A170007) Computational and Applied Mathematics | (S01) Applied Mathematics | P | Czech | Ostrava | Choice-compulsory type B | study plan | |||||

2019/2020 | (N0541A170007) Computational and Applied Mathematics | (S01) Applied Mathematics | K | Czech | Ostrava | Choice-compulsory type B | study plan |

Block name | Academic year | Form of study | Study language | Year | W | S | Type of block | Block owner |
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2021/2022 Winter |

2020/2021 Winter |