Lecture 3.
Absolute and Relative
Error
Today I discussed the
notions of absolute and relative error. I illustrated these concepts using our
simple decimal floating point number system. Through examples we verified that
the relative error of a floating point number is at most eps.
Floating Point
Arithmetic and Subtractive
Cancellation
We looked at the
expression
ex1 = 3* (4/3
-1)
The distributive law implies that
this equals ex2 = 12/3 -3. However typing these expressions into Matlab yields
two different results. The error involved in computing ex1 turns out to be eps.
I the showed that the relative
error of 2 - ex1 is eps. However the relative error of (10^6 + 1) - 10^6* ex1 is
a million times bigger, illustrating the effects of subtractive cancelation.
Taylor's
Theorem
I flashed the formulas
for Taylor's theorem while giving a pep talk on appreciating mathematics. We
will look at Taylor's theorem in earnest next week. See the readings for week
two and read up on this as preparation for next weeks
lecture(s).
Posted: Fri - September 15, 2006 at 03:36 PM