
Section 8.3 The ubiquity of the scalar product in numerical analysis 257
In short: Interval arithmetic brings guarantees and mathematics into computing,
while the exact scalar product brings speed, dynamic precision, and accuracy. A com-
bination of both is what is needed from a modern computer.
8.3 The ubiquity of the scalar product in numerical
analysis
In numerical analysis the scalar or dot product is ubiquitous. It is not merely a funda-
mental operation in all the product spaces mentioned above. The process of residual or
defect correction, or of iterative refinement, is composed of scalar products. There are
well-known limitations to these proc ...