{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

workshop 1

# workshop 1 - — 1 — Problem Derivatives re-visited In...

This preview shows pages 1–2. Sign up to view the full content.

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: — 1 — Problem. Derivatives re-visited In engineering and scientific problems data are often “noisy” – even if the tabulated function f ( x ) is supposed to be nice and smooth, errors in measurement and computation might affect the result. Often the errors in measuring f are independently random and roughly of the same magnitude for each x . If that is the case and you have some additional information about function f (e.g., f might be known to be linear, or quadratic, or exponential, etc.), then you can recover “the most likely” true values of the smooth f from your noisy measurements. Here we address a somewhat different problem: detecting an isolated error in the tabulation of a smooth function. We will assume that all f ( x i ) ’s are listed correctly, except for one x j for which f ( x j ) was computed or measured with much less precision. Our task (to find x j among the benign x i ’s) is not as easy as it sounds. Table 1 on the next page contains values of a smooth function measured at 11 equidistant points on the interval [2 , 3] . Ten of these measurements were carried out very accurately; the eleventh value was contaminated with a relatively large error (on the order...
View Full Document

{[ snackBarMessage ]}

### Page1 / 6

workshop 1 - — 1 — Problem Derivatives re-visited In...

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online