Chapter 9
Sample applications
Floating-point arithmetic is the fast way to perform scientific and engi-
neering calculations. Today, individualfloating-pointoperations are max-
imally accurate in general. However, after as few as two operations, the
computed result might be completely wrong. Computers can now carry
out up to 10
14
or 10
15
floating-point operations in a second. Therefore
particular attention must be paid to the reliability of the computed re-
sults. Conventional error analysis is impossible for computation at such
speed.
Numerical analysts have devised algorithms and techniques which
make it possible for the computer itself to verify the correctness of com-
puted results, and even to establish the existence and uniqueness of a so-
lution wit ...