SubjectsSubjects(version: 945)
Course, academic year 2023/2024
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Solution of Nonlinear Algebraic Equations - NMNV501
Title: Řešení nelineárních algebraických rovnic
Guaranteed by: Department of Numerical Mathematics (32-KNM)
Faculty: Faculty of Mathematics and Physics
Actual: from 2021
Semester: winter
E-Credits: 5
Hours per week, examination: winter s.:2/2, C+Ex [HT]
Capacity: unlimited
Min. number of students: unlimited
4EU+: no
Virtual mobility / capacity: no
State of the course: not taught
Language: Czech, English
Teaching methods: full-time
Teaching methods: full-time
Guarantor: doc. RNDr. Václav Kučera, Ph.D.
Class: M Mgr. MOD
M Mgr. MOD > Povinně volitelné
M Mgr. NVM
M Mgr. NVM > Povinné
Classification: Mathematics > Numerical Analysis
Incompatibility : NMNV503, NNUM021
Interchangeability : NMNV503, NNUM021
Is interchangeable with: NNUM021
In complex interchangeability with: NMNV503
In complex incompatibility with: NMNV503
Annotation -
Last update: T_KNM (11.05.2015)
The course deals with theoretical and practical aspects of the numerical solution of nonlinear equations and their systems. The emphasis is on Newton's method and its modifications. Students will also test the algorithms practically.
Course completion requirements -
Last update: doc. RNDr. Václav Kučera, Ph.D. (08.10.2017)

Credit for the exercise is granted for continuous activity at the exercise and continuous homework throughout the semester.

Literature -
Last update: KUCERA4 (28.04.2015)

J. M. Ortega, W. C. Rheinboldt: Iterative solution of nonlinear equations in several variables. Academic Press new York and London, 1970.

C. T. Kelley: Solving Nonlinear Equations with Newton's Method. Philadelphia, SIAM 2003.

A. Ostrowski: Solution of Equations and Systems of Equations. Academic Press, New York 1960; second edition, 1966.

P. Henrici: Elements of Numerical Analysis. John Wiley and Sons, Inc. 1964.

P. Deufelhard: Newton Methods for Nonlinear Problems. Springer-Verlag Berlin Heidelberg, 2004.

Teaching methods -
Last update: doc. RNDr. Václav Kučera, Ph.D. (29.09.2020)

Teaching in the academic year 2020/21: In the case of distance learning, the lecture and exercises will be held on the ZOOM platform at the time according to the schedule. Materials for the lecture will be available at in the directory home/kucera/Nonlinear Algebraic Equations.

Requirements to the exam -
Last update: doc. RNDr. Václav Kučera, Ph.D. (08.10.2017)

The exam is oral. The examination requirements are given by the topics in the syllabus, in the extent to which they they were taught in course.

Syllabus -
Last update: KUCERA4 (28.04.2015)

Nonlinear systems of equations, existence theorems (Banach, Brouwer, Zarantonello).

Convergence speed, orders of convergence.

Scalar equations, basic methods (bisection, fixed point iteration, regula falsi).

Newton and secant methods, local convergence, types of failure, difference approximation.

Sophisticated and hybrid algorithms (Muller's method, inverse quadratic interpolation, Brent's method).

Systems of equations, properties, Ostrowski theorem.

Newton's method for systems, local convergence, quasi-Newton approaches.

Global convergence, continuation methods.

Entry requirements -
Last update: doc. RNDr. Václav Kučera, Ph.D. (16.05.2018)

General knowledge of mathematical analysis and linear algebra.

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