Algorithms for finding zeros and extrema of functions
without calculating derivatives
6. R. P. Brent,
Algorithms for finding zeros and extrema of functions
without calculating derivatives,
Report TR CS 198, DCS, Stanford (February 1971), 313 pp.
Report: microfiche available from NTIS, reference #AD726170
(for excerpts see below).
Abstract
This report 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.
Comment
This is the author's Ph.D. thesis.
A revision was published as:
Algorithms for Minimization without Derivatives,
Prentice-Hall, Englewood Cliffs, New Jersey, 1973.
Excerpts from the Report
These are gif page images, 800×1100 pixels:
cover;
preface;
contents part 1,
contents part 2;
last page.
The above excerpts are also available in a single
pdf file (230K).
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