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Brent R.P. Algorithms for Minimization without Derivatives

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Brent R.P. Algorithms for Minimization without Derivatives
Englewood Cliffs, New Jersey: Prentice-Hall, 1973. — 195 p. — ISBN 0-13-022335-2.
This monograph describes and analyzes some practical methods for finding approximate zeros and minima of functions, using only function (not derivative) evaluations. Contents include:
The use of successive interpolation for finding simple zeros of a function and its derivatives.
An algorithm with guaranteed convergence for finding a zero of a function.
An algorithm with guaranteed convergence for finding a minimum of a function of one variable.
Global minimization given an upper bound on the second derivative.
A new algorithm for minimizing a function of several variables without calculating derivatives.
Computer programs which implement these algorithms.
Particular attention is paid to giving implementations which are reliable in the presence of rounding errors and floating-point under/overflow.
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