TAILIEUCHUNG - Lập Trình C# all Chap "NUMERICAL RECIPES IN C" part 56

Tham khảo tài liệu 'lập trình c# all chap "numerical recipes in c" part 56', công nghệ thông tin phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | 200 Chapter5. Evaluation ofFunctions define NFEW . define NMANY . float c d e a b Economize NMANY power series coefficients e in the range a b into NFEW coefficients d . c vector 0 NMANY-1 d vector 0 NFEW-1 e vector 0 NMANY-1 pcshft b-a b-a e NMANY pccheb e c NMANY . Here one would normally examine the Chebyshev coefficients c to decide how small NFEW can be. chebpc c d NFEW pcshft a b d NFEW In our example by the way the 8th through 10th Chebyshev coefficients turn out to be on the order of 7 x 10-6 3 x 10-7 and 9 x 10-9 so reasonable truncations for single precision calculations are somewhere in this range yielding a polynomial with 8 -10 terms instead of the original 13. Replacing a 13-term polynomial with a say 10-term polynomial without any loss of accuracy that does seem to be getting something for nothing. Is there some magic in this technique Not really. The 13-term polynomial defined a function f x . Equivalent to economizing the series we could instead have evaluated f x at enough points to construct its Chebyshev approximation in the interval of interest by the methods of . We would have obtained just the same lower-order polynomial. The principal lesson is that the rate of convergence of Chebyshev coefficients has nothing to do with the rate of convergence of power series coefficients and it is the former that dictates the number of terms needed in a polynomial approximation. A function might have a divergent power series in some region of interest but if the function itself is well-behaved it will have perfectly good polynomial approximations. These can be found by the methods of but not by economization of series. There is slightly less to economization of series than meets the eye. CITED REFERENCES AND FURTHER READING Acton . 1970 Numerical Methods That Work 1990 corrected edition Washington Mathematical Association of America Chapter 12. Arfken G. 1970 Mathematical Methods for Physicists 2nd .

• Kỹ thuật lập trình
• thủ thuật lập trình
• tư liệu lập trình
• ngôn ngữ lập trình
• hướng dẫn lập trình
• kĩ năng lập trình
• kỹ thuật lập trình
• kỹ năng lập trình
• bí quyết lập trình
• phương pháp lập trình
• kĩ thuật lập trình
• AutoIT