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Course, academic year 2018/2019
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Solution of Nonlinear Algebraic Equations - NMNV501
Title in English: Řešení nelineárních algebraických rovnic
Guaranteed by: Department of Numerical Mathematics (32-KNM)
Faculty: Faculty of Mathematics and Physics
Actual: from 2018
Semester: winter
E-Credits: 5
Hours per week, examination: winter s.:2/2 C+Ex [hours/week]
Capacity: unlimited
Min. number of students: unlimited
State of the course: taught
Language: Czech, English
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 : NNUM021
Interchangeability : NNUM021
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.

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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