HP 35s Scientific Calculator Manuel d'utilisateur télécharger pdf (Page 338)

E-2 More about Integration

As explained in chapter 8, the uncertainty of the final approximation is a number

derived from the display format, which specifies the uncertainty for the function. At

the end of each iteration, the algorithm compares the approximation calculated

during that iteration with the approximations calculated during two previous

iterations. If the difference between any of these three approximations and the other

two is less than the uncertainty tolerable in the final approximation, the calculation

ends, leaving the current approximation in the X–register and its uncertainty in the

Y–register.

It is extremely unlikely that the errors in each of three successive approximations —

that is, the differences between the actual integral and the approximations — would

all be larger than the disparity among the approximations themselves.

Consequently, the error in the final approximation will be less than its uncertainty

(provided that f(x) does not vary rapidly). Although we can't know the error in the

final approximation, the error is extremely unlikely to exceed the displayed

uncertainty of the approximation. In other words, the uncertainty estimate in the Y–

approximation and the actual integral.

Conditions That Could Cause Incorrect Results

Although the integration algorithm in the HP 35s is one of the best available, in

certain situations it — like all other algorithms for numerical integration — might

give you an incorrect answer. The possibility of this occurring is extremely remote.

The algorithm has been designed to give accurate results with almost any smooth

function. Only for functions that exhibit extremely erratic behavior is there any

substantial risk of obtaining an inaccurate answer. Such functions rarely occur in

problems related to actual physical situations; when they do, they usually can be

recognized and dealt with in a straightforward manner.

Unfortunately, since all that the algorithm knows about f(x) are its values at the

sample points, it cannot distinguish between f(x) and any other function that agrees

with f(x) at all the sample points. This situation is depicted below, showing (over a

portion of the interval of integration) three functions whose graphs include the many

sample points in common.

1 2 ... 333 334 335 336 337 338 339 340 341 342 343 ... 381 382

Pas de commentaire

HP 35s Scientific Calculator Manuel d'utilisateur Page 338