470-4504/03 – Iterative Methods (IM)

Gurantor departmentDepartment of Applied MathematicsCredits6
Subject guarantorIng. Simona Bérešová, Ph.D.Subject version guarantorIng. Simona Bérešová, Ph.D.
Study levelundergraduate or graduateRequirementChoice-compulsory type B
YearSemesterwinter
Study languageCzech
Year of introduction2019/2020Year of cancellation
Intended for the facultiesFEIIntended for study typesFollow-up Master
Instruction secured by
LoginNameTuitorTeacher giving lectures
DOM0015 Ing. Simona Bérešová, Ph.D.
Extent of instruction for forms of study
Form of studyWay of compl.Extent
Full-time Credit and Examination 2+2
Part-time Credit and Examination 10+10

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

Way of continuous check of knowledge in the course of semester

Obhajoba semestrálního projektu. Zkouška písemná a ústní.

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

Part-time form (validity from: 2019/2020 Winter semester)
Task nameType of taskMax. number of points
(act. for subtasks)
Min. number of pointsMax. počet pokusů
Credit and Examination Credit and Examination 100 (100) 51
        Credit Credit 30  15
        Examination Examination 70  36 3
Mandatory attendence participation: Participation in exercises is obligatory (80%)

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

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Occurrence in study plans

Academic yearProgrammeBranch/spec.Spec.ZaměřeníFormStudy language Tut. centreYearWSType 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

Occurrence in special blocks

Block nameAcademic yearForm of studyStudy language YearWSType of blockBlock owner

Assessment of instruction



2021/2022 Winter
2020/2021 Winter