TAILIEUCHUNG - Lập Trình C# all Chap "NUMERICAL RECIPES IN C" part 174

Tham khảo tài liệu 'lập trình c# all chap "numerical recipes in c" part 174', công nghệ thông tin phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | 420 Chapter 10. Minimization or Maximization of Functions CITED REFERENCES AND FURTHER READING Brent . 1973 AlgorithmsforMinimizationwithoutDerivatives Englewood Cliffs NJ Prentice- Hall Chapter 7. 1 Acton . 1970 Numerical Methods That Work 1990 corrected edition Washington Mathe- matical Association of America pp. 464-467. 2 Jacobs . ed. 1977 The State of the Art in Numerical Analysis London Academic o Press pp. 259-262. g 2 Sample page from NUMERICAL RECIPES IN C THE ART OF SCIENTIFIC COMPUTING ISBN 0-521-43108-5 Cfl _K O 3 x-x Q Q O 3- V V 0 o Conjugate Gradient Methods in f o Multidimensions ftp o M Q g CO O C We consider now the case where you are able to calculate at a given N- g 2 dimensional point P not just the value of a function f P but also the gradient g vector of first partial derivatives V f P . M -S is A rough counting argument will show how advantageous it is to use the gradient z K p information Suppose that the function f is roughly approximated as a quadratic form as above in equation f x c b x i x A x Then the number of unknown parameters in f is equal to the number of free parameters in A and b which is 1N N 1 which we see to be of order N2. g Changing any one of these parameters can move the location of the minimum. Therefore we should not expect to be able to find the minimum until we have m collected an equivalent information content of order N2 numbers. In the direction set methods of we collected the necessary information by jj making on the order of N2 separate line minimizations each requiring a few but a - sometimes a big few function evaluations. Now each evaluation of the gradient g- . 5 will bring us N new components of information. If we use them wisely we should need to make only of order N separate line minimizations. That is in fact the case for the algorithms in this section and the next. A factor of N improvement in computational speed is not necessarily implied. O As a rough estimate we .

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