CMSC/AMSC 460 Fall 2007
Homework 1
Due Tuesday, September 18, before class begins
10 points
Under fixed point arithmetic, if we add nnumbers, then either we get the
exact answer or we get an ”overflow” error.
Under floating point arithmetic, this is not true. We probably get an
approximation to the exact answer, although we could possibly get the exact
answer or overflow.
Consider the three examples in the program hw1.m. You might want
to play with the program, changing nor hor computing the difference be-
tween the computed sums and the true ones in order to understand what is
happening.
(a) (1) Is sum1 equal to the true value? If not, why not? (Be specific: it
is not enough to say, “Round-off caused the error.” If sum1 is not exact, in
what part of the calculation did the error arise?)
(b) (3) Are sum2 and sum3 equal to the true value? If not, why not?
And why aren’t they equal to each other?
(c) (3) Are sum4 and sum5 equal to the true value? If not, why not? And
why aren’t they equal to each other?
(d) (3) Given nnumbers to add, what ordering do you advise using to
keep round-off error small?
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