# Application of iterative algorithm $(\theta_n,w_n)$ converging to $\{(\theta,\theta):\theta \in \Bbb R\}$

I have a iterative algorithm $$(\theta_n,w_n)$$ which I am showing converges to $$\{(\theta,\theta):\theta \in \Bbb R\}$$. The iterative algorithm is of the form : $$\theta_{n+1} = \theta_n + a(n)[h(\theta_n,w_n)]$$, $$w_{n+1} = w_n + b(n)[g(\theta_n,w_n)]$$

I want to know whether there could be any practical application of this.

• At this level of generality, it is impossible to answer the question. What is your algorithm doing? What problem is it solving? – Yuval Filmus Feb 19 '19 at 11:25
• @YuvalFilmus: I am showing that it converges to the 45 degree line. I am looking for a situation where these things will be useful. – applied_math Feb 19 '19 at 11:32
• Still too general. It's not even clear what you mean by "coupled iterative algorithm". – Yuval Filmus Feb 19 '19 at 11:34
• @YuvalFilmus: There are two recursions $\theta_n$ and $w_n$. – applied_math Feb 19 '19 at 11:40
• @applied_math "The iteraive algorithm is of the form". Which form? Please include a specific example in the question. – John L. Feb 19 '19 at 11:55