Is there any convenient notation for a vector entry j at iteration step i? I have a stupid question: I'm writing a master thesis and I have to describe an iterative method of an algorithm. The method uses vectors which are manipulated at each iteration step. Now my question: is there any convenient method of writing for example entry $j$ of vector $\mathbf{a}$ on iteration step $k$? I thought of $\mathbf{a}^k_j$ or $(\mathbf{a}_k)_j$ or $\mathbf{a^{\langle k \rangle}_j}$ but these are all quite ambiguous. Any ideas? With kind regards, Filip M

Presumably you already have a notation to indicate the $j$-the element of _any_ vector $\mathbf{v}$, and you should be consistent with this.

Also, for this particular algorithm (or for iterative algorithms in general), you probably have a way to indicate the value of variable $x$ during the $k$-th iteration. You ought to be consistent with this, too.

My personal choices would be:

(1) $\mathbf{v}[j]$ denotes the $j$-the element of the vector $\mathbf{v}$.

(2) $x_k$ denotes the value of the variable $x$ during the $k$-th iteration.

So, putting these two together, $\mathbf{a}_k[j]$ or $\mathbf{a}[j]_k$ is the value of $\mathbf{a}[j]$ during the $k$-th iteration. I prefer the former.

There are many other choices, of course; it's the consistency that's important, in my view.