Tham khảo tài liệu 'lập trình c# all chap "numerical recipes in c" part 52', công nghệ thông tin phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | 198 Chapter5. Evaluation ofFunctions void pcshft float a float b float d int n Polynomial coefficient shift. Given a coefficient array d this routine generates a coefficient array g such that Pn odfcyk Pn 1 gkxk where x and y are related by . the interval 1 y 1 is mapped to the interval a x b. The array g is returned in d. int k j float fac cnst cnst b-a fac cnst for j 1 j n j d j fac fac cnst cnst a b for j 0 j n-2 j for k n-2 k j k d k - cnst d k 1 First we rescale by the factor const. .which is then redefined as the desired shift. We accomplish the shift by synthetic division. Synthetic division is a miracle of high-school algebra. If you never learned it go do so. You won t be sorry. CITED REFERENCES AND FURTHER READING Acton . 1970 Numerical Methods That Work 1990 corrected edition Washington Mathematical Association of America pp. 59 182-183 synthetic division . Economization ofPower Series One particular application of Chebyshev methods the economization ofpower series is an occasionally useful technique with a flavor of getting something for nothing. Suppose that you are already computing a function by the use of a convergent power series for example r r2 r3 fX 1 - 3 5 - 7 This function is actually sin y x fx but pretend you don t know that. You might be doing a problem that requires evaluating the series many times in some particular interval say 0 2 2 . Everything is fine except that the series requires a large number of terms before its error approximated by the first neglected term say is tolerable. In our example with x 2 2 the first term smaller than 10 7 is x13 27 . This then approximates the error of the finite series whose last term is x12 25 . Notice that because of the large exponent in x13 the error is much smaller than 10 7 everywhere in the interval except at the very largest values of x. This is the feature that allows economization if we are willing to let the error elsewhere in the interval rise
