CS3414 Afterclass Notes --- 22 May, 2002

Returning to the big issue of accuracy for a few minutes, we talked about three things: conditioning, stability, and floating point.

Conditioning: a property of a problem. Is the true answer sensitive to small changes in the data or problem?

Stability: a property of an algorithm, as implemented. Is the computed answer sensitive to small changes introduced somewhere along the way? (These changes could be in the initial data, from floating point, etc.)

Floating point representation and round-off error. (See the handout and Chapter 2 of Cheney and Kincaid for more details.)

IEEE standard for floating point representation.
Implications of floating point representation, e.g., no more than 6 significant decimal digits of accuracy in a 32 bit calculation.
Propagation of floating point error in floating point arithmetic.

We then began our discussion of the first major problem to be studied this semester---root finding (Chapter 3). We looked at an example problem where root finding can come in handy, and we posed this problem as a mathematical problem g(x)=0.