# Wikidata:Property proposal/convergence rate

### order of convergence (changed from "convergence rate")Edit

Originally proposed at Wikidata:Property proposal/Natural science

#### MotivationEdit

Well-posed numerical methods (theoretically) converge to the exact solution as . For discretized methods, is the grid size of the discretization and . For iterative methods, could be the number of iterations and . Alternatively, for iterative numerical methods for solving differential equations, is the tiem-step size and . In each case, there is an upper bound on the on the error of the method as a function of as . It would be useful to have methods categorized according to this property.

Specifically, I am proposing that we add a property whose subject is the big-O order of convergence for the method. That is, we would set <order of convergence> <g(n)> where g(n) is a function such if

There are a lot of definitions that are used similarly, so I'm going to list them here and we'll try to sort them out.

- Rate of convergence: if a sequence converges linearly, is called the
*rate of convergence* - If a sequence converges to a limit, then r

The following excerpt from [4] provides clear definitions of order and rate of convergences.

- "whether this iteration will converge, and, if so, the rate of convergence. Specifically we use the following to represent how quickly the error \(e_{n}=x_{n}-x^{*}\) converges to zero: Here \(p \geq 1\) is called the order of convergence, the constant \(\mu\) is the rate of comergence or asymptotic error constant."

I think it makes sense to create an order of convergence (OC) property, but not a rate of convergence (RC). The reason for this, is that OC is (1) a much more important property of an algorithm and (2) there will only be (in practice) a limited number of values. We'll have logarithmically, sublinear, linear, quadratic, cubic, quartic, and maybe a few more. Whereas RC could be any real number.

The-erinaceous-one (talk) 07:47, 31 July 2020 (UTC)