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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 2016 to 2017
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:	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 :	NNUM021
Interchangeability :	NNUM021
Is interchangeable with:	NNUM021

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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.

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.

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.