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.
