470-6506/02 – Iterative Methods (IMD)

Gurantor department	Department of Applied Mathematics	Credits	10
Subject guarantor	doc. Ing. David Horák, Ph.D.	Subject version guarantor	doc. Ing. David Horák, Ph.D.
Study level	postgraduate	Requirement	Choice-compulsory type B
Year		Semester	winter + summer
		Study language	English
Year of introduction	2015/2016	Year of cancellation	2024/2025
Intended for the faculties	FS, FAST, FMT, HGF, FEI	Intended for study types	Doctoral

Instruction secured by
Login	Name	Tuitor	Teacher giving lectures
HOR33	doc. Ing. David Horák, Ph.D.

Extent of instruction for forms of study
Form of study	Way of compl.	Extent
Full-time	Examination	28+0
Part-time	Examination	28+0

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

Additional study materials

Study supports in the EduDocs system

Way of continuous check of knowledge in the course of semester

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

E-learning

Consultation through MS Teams.

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

Full-time form (validity from: 2015/2016 Winter semester, validity until: 2024/2025 Summer semester)

Task name	Type of task	Max. number of points (act. for subtasks)	Min. number of points	Max. počet pokusů
Examination	Examination			3

Mandatory attendence participation:

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Conditions for subject completion and attendance at the exercises within ISP:

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Occurrence in study plans

Academic year	Programme	Branch/spec.	Form	Study language	Tut. centre	Type of duty
2024/2025	(P0712D130003) Chemical and environmental engineering		P	English	Ostrava	Compulsory	study plan
2024/2025	(P0719D270006) Transport and Material Handling		P	English	Ostrava	Choice-compulsory type B	study plan
2024/2025	(P0719D270006) Transport and Material Handling		K	English	Ostrava	Choice-compulsory type B	study plan
2024/2025	(P0533D110006) Applied Physics		P	English	Ostrava	Choice-compulsory type B	study plan
2024/2025	(P0533D110006) Applied Physics		K	English	Ostrava	Choice-compulsory type B	study plan
2024/2025	(P0541D170006) Computational and Applied Mathematics		P	English	Ostrava	Choice-compulsory type B	study plan
2023/2024	(P0533D110006) Applied Physics		K	English	Ostrava	Choice-compulsory type B	study plan
2023/2024	(P0533D110006) Applied Physics		P	English	Ostrava	Choice-compulsory type B	study plan
2023/2024	(P0541D170006) Computational and Applied Mathematics		P	English	Ostrava	Choice-compulsory type B	study plan
2023/2024	(P0719D270006) Transport and Material Handling		K	English	Ostrava	Choice-compulsory type B	study plan
2023/2024	(P0719D270006) Transport and Material Handling		P	English	Ostrava	Choice-compulsory type B	study plan
2023/2024	(P0712D130003) Chemical and environmental engineering		P	English	Ostrava	Compulsory	study plan
2023/2024	(P1807) Computer Science, Communication Technology and Applied Mathematics	(1103V036) Computational and Applied Mathematics	P	English	Ostrava	Choice-compulsory	study plan
2023/2024	(P1807) Computer Science, Communication Technology and Applied Mathematics	(1103V036) Computational and Applied Mathematics	K	English	Ostrava	Choice-compulsory	study plan
2022/2023	(P0533D110006) Applied Physics		P	English	Ostrava	Choice-compulsory type B	study plan
2022/2023	(P0533D110006) Applied Physics		K	English	Ostrava	Choice-compulsory type B	study plan
2022/2023	(P1807) Computer Science, Communication Technology and Applied Mathematics	(1103V036) Computational and Applied Mathematics	P	English	Ostrava	Choice-compulsory	study plan
2022/2023	(P1807) Computer Science, Communication Technology and Applied Mathematics	(1103V036) Computational and Applied Mathematics	K	English	Ostrava	Choice-compulsory	study plan
2022/2023	(P0719D270006) Transport and Material Handling		P	English	Ostrava	Choice-compulsory type B	study plan
2022/2023	(P0719D270006) Transport and Material Handling		K	English	Ostrava	Choice-compulsory type B	study plan
2022/2023	(P0712D130003) Chemical and environmental engineering		P	English	Ostrava	Compulsory	study plan
2022/2023	(P0541D170006) Computational and Applied Mathematics		P	English	Ostrava	Choice-compulsory type B	study plan
2021/2022	(P0719D270006) Transport and Material Handling		K	English	Ostrava	Choice-compulsory type B	study plan
2021/2022	(P0719D270006) Transport and Material Handling		P	English	Ostrava	Choice-compulsory type B	study plan
2021/2022	(P0533D110006) Applied Physics		P	English	Ostrava	Choice-compulsory type B	study plan
2021/2022	(P0533D110006) Applied Physics		K	English	Ostrava	Choice-compulsory type B	study plan
2021/2022	(P0712D130003) Chemical and environmental engineering		P	English	Ostrava	Compulsory	study plan
2021/2022	(P0541D170006) Computational and Applied Mathematics		P	English	Ostrava	Choice-compulsory type B	study plan
2021/2022	(P1807) Computer Science, Communication Technology and Applied Mathematics	(1103V036) Computational and Applied Mathematics	P	English	Ostrava	Choice-compulsory	study plan
2021/2022	(P1807) Computer Science, Communication Technology and Applied Mathematics	(1103V036) Computational and Applied Mathematics	K	English	Ostrava	Choice-compulsory	study plan
2020/2021	(P0533D110006) Applied Physics		K	English	Ostrava	Choice-compulsory type B	study plan
2020/2021	(P0533D110006) Applied Physics		P	English	Ostrava	Choice-compulsory type B	study plan
2020/2021	(P0541D170006) Computational and Applied Mathematics		P	English	Ostrava	Choice-compulsory type B	study plan
2020/2021	(P1807) Computer Science, Communication Technology and Applied Mathematics	(1103V036) Computational and Applied Mathematics	P	English	Ostrava	Choice-compulsory	study plan
2020/2021	(P1807) Computer Science, Communication Technology and Applied Mathematics	(1103V036) Computational and Applied Mathematics	K	English	Ostrava	Choice-compulsory	study plan
2020/2021	(P0719D270006) Transport and Material Handling		P	English	Ostrava	Choice-compulsory type B	study plan
2020/2021	(P0719D270006) Transport and Material Handling		K	English	Ostrava	Choice-compulsory type B	study plan
2019/2020	(P0533D110006) Applied Physics		P	English	Ostrava	Choice-compulsory type B	study plan
2019/2020	(P0541D170006) Computational and Applied Mathematics		P	English	Ostrava	Choice-compulsory type B	study plan
2019/2020	(P0533D110006) Applied Physics		K	English	Ostrava	Choice-compulsory type B	study plan
2019/2020	(P1807) Computer Science, Communication Technology and Applied Mathematics	(1103V036) Computational and Applied Mathematics	P	English	Ostrava	Choice-compulsory	study plan
2019/2020	(P1807) Computer Science, Communication Technology and Applied Mathematics	(1103V036) Computational and Applied Mathematics	K	English	Ostrava	Choice-compulsory	study plan
2018/2019	(P1807) Computer Science, Communication Technology and Applied Mathematics	(1103V036) Computational and Applied Mathematics	P	English	Ostrava	Choice-compulsory	study plan
2018/2019	(P1807) Computer Science, Communication Technology and Applied Mathematics	(1103V036) Computational and Applied Mathematics	K	English	Ostrava	Choice-compulsory	study plan
2017/2018	(P1807) Computer Science, Communication Technology and Applied Mathematics	(1103V036) Computational and Applied Mathematics	P	English	Ostrava	Choice-compulsory	study plan
2017/2018	(P1807) Computer Science, Communication Technology and Applied Mathematics	(1103V036) Computational and Applied Mathematics	K	English	Ostrava	Choice-compulsory	study plan
2016/2017	(P1807) Computer Science, Communication Technology and Applied Mathematics	(1103V036) Computational and Applied Mathematics	P	English	Ostrava	Choice-compulsory	study plan
2016/2017	(P1807) Computer Science, Communication Technology and Applied Mathematics	(1103V036) Computational and Applied Mathematics	K	English	Ostrava	Choice-compulsory	study plan
2015/2016	(P1807) Computer Science, Communication Technology and Applied Mathematics	(1103V036) Computational and Applied Mathematics	P	English	Ostrava	Choice-compulsory	study plan
2015/2016	(P1807) Computer Science, Communication Technology and Applied Mathematics	(1103V036) Computational and Applied Mathematics	K	English	Ostrava	Choice-compulsory	study plan

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