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Last update: doc. RNDr. Václav Kučera, Ph.D. (19.12.2018)
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Last update: doc. RNDr. Václav Kučera, Ph.D. (19.12.2018)
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.
R. Fletcher, Practical Methods of Optimization, 2nd edition Wiley 1987, (republished 2000).
D. G. Luenberger and Y. Ye, Linear and Nonlinear Programming, Third edition. Springer, New York, MA, 2008.
J. Nocedal and S. Wright, Numerical Optimization, Second edition, Springer Verlag 2006.
J. E. Dennis, Jr. and Robert B. Schnabel, Numerical Methods for Unconstrained Optimization and Nonlinear Equations, SIAM 1996, originally published in 1983. |
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Last update: doc. RNDr. Václav Kučera, Ph.D. (20.12.2018)
Basic numerical methods for solving scalar nonlinear equations (Newton's method and secant method), local convergence, order of convergence. More advanced methods (Muller's method, inverse quadratic interpolation, Brent's method). Solution of systems of nonlinear equations, Newton's method, quasi-Newtonian methods. Global convergence, continuation methods. Theory of unconstrained optimization (necessary and sufficient conditions, role of convexity). Line search - the search for minima in the given descent direction (Goldstein, Armijo, Wolfe conditions). Basic descent methods (the method of steepest descent and the Newton method), conjugate direction methods (the nonlinear conjugate gradient method), Quasi-Newton methods (rank-one update, DFP, BFGS, the Broyden family), Trust-region methods, dogleg. Least-squares problems (the Gauss-Newton and the Levenberg-Marquart method). |