HP 15C Manuale Utente Scaricare il pdf (Pagina 250)

250 Appendix E: A Detailed Look at f

With this number of sample points, the algorithm will calculate the same

approximation for the integral of any of the functions shown. The actual

integrals of the functions shown with solid lines are about the same, so the

approximation will be fairly accurate if f(x) is one of these functions.

However, the actual integral of the function shown with a dashed line is

quite different from those of the others, so the current approximation will be

rather inaccurate if f(x) is this function.

The f algorithm comes to know the general behavior of the function by

sampling the function at more and more points. If a fluctuation of the

function in one region is not unlike the behavior over the rest of the interval

of integration, at some iteration the algorithm will likely detect the

fluctuation. When this happens, the number of sample points is increased

until successive iterations yield approximations that take into account the

presence of the most rapid, but characteristic, fluctuations.

For example, consider the approximation of







.dx

1 2 ... 245 246 247 248 249 250 251 252 253 254 255 ... 287 288

Nessun commento

HP 15C Manuale Utente Pagina 250