470-6506/01 – Iterative Methods (IMD)

Gurantor departmentDepartment of Applied MathematicsCredits10
Subject guarantorprof. RNDr. Radim Blaheta, CSc.Subject version guarantorprof. RNDr. Radim Blaheta, CSc.
Study levelpostgraduateRequirementChoice-compulsory
YearSemesterwinter + summer
Study languageCzech
Year of introduction2010/2011Year of cancellation
Intended for the facultiesFS, HGF, FAST, FEI, FMTIntended for study typesDoctoral
Instruction secured by
LoginNameTuitorTeacher giving lectures
BLA19 prof. RNDr. Radim Blaheta, CSc.
Extent of instruction for forms of study
Form of studyWay of compl.Extent
Full-time Examination 28+0
Combined 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

Way of continuous check of knowledge in the course of semester

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

E-learning

Další požadavky na studenta

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

Combined form (validity from: 2013/2014 Winter semester)
Task nameType of taskMax. number of points
(act. for subtasks)
Min. number of points
Examination Examination  
Mandatory attendence parzicipation:

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Academic yearProgrammeField of studySpec.FormStudy language Tut. centreYearWSType of duty
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

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