470-6506/02 – Iterative Methods (IMD)
| 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 type B |
| Year | | Semester | winter + summer |
| | Study language | English |
| Year of introduction | 2015/2016 | Year of cancellation | |
| Intended for the faculties | FAST, FMT, FEI, FS, HGF | Intended for study types | Doctoral |
Subject aims expressed by acquired skills and competences
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.
Teaching methods
Lectures
Project work
Summary
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.
Compulsory literature:
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
Recommended literature:
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
Way of continuous check of knowledge in the course of semester
The exam is written or oral. It may include a project.
E-learning
Other requirements
No additional requirements are imposed on the student.
Prerequisities
Subject has no prerequisities.
Co-requisities
Subject has no co-requisities.
Subject syllabus:
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.
Conditions for subject completion
Occurrence in study plans
Occurrence in special blocks