Gurantor department | Department of Applied Mathematics | Credits | 10 |

Subject guarantor | prof. RNDr. Radim Blaheta, CSc. | Subject version guarantor | prof. RNDr. Radim Blaheta, CSc. |

Study level | postgraduate | Requirement | Choice-compulsory |

Year | Semester | winter + summer | |

Study language | Czech | ||

Year of introduction | 2010/2011 | Year of cancellation | |

Intended for the faculties | HGF, FMT, FEI, FS, FAST | Intended for study types | Doctoral |

Instruction secured by | |||
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Login | Name | Tuitor | Teacher giving lectures |

BLA19 | prof. RNDr. Radim Blaheta, CSc. |

Extent of instruction for forms of study | ||
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Form of study | Way of compl. | Extent |

Full-time | Examination | 28+0 |

Combined | Examination | 28+0 |

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

Lectures

Project work

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

The exam is written or oral. It may include a project.

No additional requirements are imposed on the 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.

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

Examination | Examination |

Show history

Academic year | Programme | Field of study | Spec. | Form | Study language | Tut. centre | Year | W | S | Type of duty | |
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2019/2020 | (P3909) Process engineering | (3909V003) Process engineering | P | Czech | Ostrava | Choice-compulsory | study plan | ||||

2019/2020 | (P3909) Process engineering | (3909V003) Process engineering | K | Czech | Ostrava | Choice-compulsory | study plan | ||||

2019/2020 | (P0533D110005) Applied Physics | P | Czech | Ostrava | Choice-compulsory type B | study plan | |||||

2019/2020 | (P0712D130002) Chemical and environmental engineering | P | Czech | Ostrava | Choice-compulsory type B | study plan | |||||

2019/2020 | (P0541D170005) Computational and Applied Mathematics | P | Czech | Ostrava | Choice-compulsory type B | study plan | |||||

2019/2020 | (P0533D110005) Applied Physics | K | Czech | Ostrava | Choice-compulsory type B | study plan | |||||

2019/2020 | (P0541D170005) Computational and Applied Mathematics | K | Czech | Ostrava | Choice-compulsory type B | study plan | |||||

2019/2020 | (P1807) Computer Science, Communication Technology and Applied Mathematics | (1103V036) Computational and Applied Mathematics | P | Czech | Ostrava | Choice-compulsory | study plan | ||||

2019/2020 | (P1807) Computer Science, Communication Technology and Applied Mathematics | (1103V036) Computational and Applied Mathematics | K | Czech | Ostrava | Choice-compulsory | study plan | ||||

2018/2019 | (P3909) Process engineering | (3909V003) Process engineering | P | Czech | Ostrava | Choice-compulsory | study plan | ||||

2018/2019 | (P3909) Process engineering | (3909V003) Process engineering | K | Czech | Ostrava | Choice-compulsory | study plan | ||||

2018/2019 | (P1807) Computer Science, Communication Technology and Applied Mathematics | (1103V036) Computational and Applied Mathematics | P | Czech | Ostrava | Choice-compulsory | study plan | ||||

2018/2019 | (P1807) Computer Science, Communication Technology and Applied Mathematics | (1103V036) Computational and Applied Mathematics | K | Czech | Ostrava | Choice-compulsory | study plan | ||||

2017/2018 | (P3909) Process engineering | (3909V003) Process engineering | P | Czech | Ostrava | Choice-compulsory | study plan | ||||

2017/2018 | (P3909) Process engineering | (3909V003) Process engineering | K | Czech | Ostrava | Choice-compulsory | study plan | ||||

2017/2018 | (P1807) Computer Science, Communication Technology and Applied Mathematics | (1103V036) Computational and Applied Mathematics | P | Czech | Ostrava | Choice-compulsory | study plan | ||||

2017/2018 | (P1807) Computer Science, Communication Technology and Applied Mathematics | (1103V036) Computational and Applied Mathematics | K | Czech | Ostrava | Choice-compulsory | study plan | ||||

2016/2017 | (P3909) Process engineering | (3909V003) Process engineering | P | Czech | Ostrava | Choice-compulsory | study plan | ||||

2016/2017 | (P3909) Process engineering | (3909V003) Process engineering | K | Czech | Ostrava | Choice-compulsory | study plan | ||||

2016/2017 | (P1807) Computer Science, Communication Technology and Applied Mathematics | (1103V036) Computational and Applied Mathematics | P | Czech | Ostrava | Choice-compulsory | study plan | ||||

2016/2017 | (P1807) Computer Science, Communication Technology and Applied Mathematics | (1103V036) Computational and Applied Mathematics | K | Czech | Ostrava | Choice-compulsory | study plan | ||||

2015/2016 | (P3909) Process engineering | P | Czech | Ostrava | Choice-compulsory | study plan | |||||

2015/2016 | (P3909) Process engineering | (3909V003) Process engineering | P | Czech | Ostrava | Choice-compulsory | study plan | ||||

2015/2016 | (P3909) Process engineering | K | Czech | Ostrava | Choice-compulsory | study plan | |||||

2015/2016 | (P3909) Process engineering | (3909V003) Process engineering | K | Czech | Ostrava | Choice-compulsory | study plan | ||||

2015/2016 | (P1807) Computer Science, Communication Technology and Applied Mathematics | (1103V036) Computational and Applied Mathematics | P | Czech | Ostrava | Choice-compulsory | study plan | ||||

2015/2016 | (P1807) Computer Science, Communication Technology and Applied Mathematics | (1103V036) Computational and Applied Mathematics | K | Czech | Ostrava | Choice-compulsory | study plan | ||||

2014/2015 | (P3909) Process engineering | (3909V003) Process engineering | P | Czech | Ostrava | Choice-compulsory | study plan | ||||

2014/2015 | (P3909) Process engineering | (3909V003) Process engineering | K | Czech | Ostrava | Choice-compulsory | study plan | ||||

2014/2015 | (P1807) Computer Science, Communication Technology and Applied Mathematics | (1103V036) Computational and Applied Mathematics | P | Czech | Ostrava | Choice-compulsory | study plan | ||||

2014/2015 | (P1807) Computer Science, Communication Technology and Applied Mathematics | (1103V036) Computational and Applied Mathematics | K | Czech | Ostrava | Choice-compulsory | study plan | ||||

2013/2014 | (P1807) Computer Science, Communication Technology and Applied Mathematics | (1103V036) Computational and Applied Mathematics | P | Czech | Ostrava | Choice-compulsory | study plan | ||||

2013/2014 | (P1807) Computer Science, Communication Technology and Applied Mathematics | (1103V036) Computational and Applied Mathematics | K | Czech | Ostrava | Choice-compulsory | study plan | ||||

2013/2014 | (P3909) Process engineering | (3909V003) Process engineering | P | Czech | Ostrava | Choice-compulsory | study plan | ||||

2013/2014 | (P3909) Process engineering | (3909V003) Process engineering | K | Czech | Ostrava | Choice-compulsory | study plan | ||||

2012/2013 | (P1807) Computer Science, Communication Technology and Applied Mathematics | (1103V036) Computational and Applied Mathematics | P | Czech | Ostrava | Choice-compulsory | study plan | ||||

2012/2013 | (P1807) Computer Science, Communication Technology and Applied Mathematics | (1103V036) Computational and Applied Mathematics | K | Czech | Ostrava | Choice-compulsory | study plan | ||||

2011/2012 | (P1807) Computer Science, Communication Technology and Applied Mathematics | (1103V036) Computational and Applied Mathematics | P | Czech | Ostrava | Choice-compulsory | study plan | ||||

2011/2012 | (P1807) Computer Science, Communication Technology and Applied Mathematics | (1103V036) Computational and Applied Mathematics | K | Czech | Ostrava | Choice-compulsory | study plan | ||||

2010/2011 | (P1807) Computer Science, Communication Technology and Applied Mathematics | (1103V036) Computational and Applied Mathematics | P | Czech | Ostrava | Choice-compulsory | study plan | ||||

2010/2011 | (P1807) Computer Science, Communication Technology and Applied Mathematics | (1103V036) Computational and Applied Mathematics | K | Czech | Ostrava | Choice-compulsory | study plan |

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