ABSTRACT
Many people talk about algorithms, but I’m sure that many of them mean different things by that word. Let me propose my own definition here, as it applies to us. An algorithm is a mathematical recipe for estimating the value of a set of quantities x=col(x1, …, xm), which are not directly measurable, from measurements of some
other quantities y=col(y1, …, yn). 12 Many, but no means all, algorithms are iterated,
which means that you perform a calculation on the measured data to get an initial estimate of x; then, using that result, perform another calculation to get an improved estimate of x. Keep doing this a predetermined number of times, or until the sequence of estimates converges. Alternatively, an algorithm may simply perform a single calculation on the data that produces the final result. Either way, an algorithm needs to have two properties for it to be useful: 1) it must stop after a finite number of steps; and 2) it must converge to the correct solution in all but very rare instances.
