470-4504/01 – Iterative Methods (IM)
| Gurantor department | Department of Applied Mathematics | Credits | 4 |
| Subject guarantor | Ing. Simona Bérešová, Ph.D. | Subject version guarantor | prof. RNDr. Radim Blaheta, CSc. |
| Study level | undergraduate or graduate | Requirement | Optional |
| Year | | Semester | winter |
| | Study language | Czech |
| Year of introduction | 2010/2011 | Year of cancellation | 2020/2021 |
| Intended for the faculties | FEI | Intended for study types | Follow-up Master |
Subject aims expressed by acquired skills and competences
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.
Teaching methods
Lectures
Tutorials
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
Additional study materials
Way of continuous check of knowledge in the course of semester
E-learning
Other requirements
There are not defined other requirements for 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.
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.
Conditions for subject completion
Occurrence in study plans
Occurrence in special blocks
Assessment of instruction