ABSTRACT
N umerical analysis introduces a shift from working with ints and longs to floats anddoubles. This seemingly innocent transition shatters intuition from integer arithmetic, requiring adjustment of how we must think about basic algorithmic design and implementation. Unlike discrete algorithms, numerical algorithms cannot always yield exact solutions even to well-studied and well-posed problems. Operation counting no longer reigns supreme; instead, even basic techniques require careful analysis of the trade-offs among timing, approximation error, and other considerations. In this chapter, we will explore the typical factors affecting the quality of a numerical algorithm. These factors set numerical algorithms apart from their discrete counterparts.
