ART algorithm - Image Reconstruction

[nao113]

Homework Statement

Some iterative algorithms, for example, the ART algorithm, update the image very frequently. For those algorithms, the processing order of the data subsets is important. In this problem, we use the ART algorithm to graphically solve a system of linear equations {𝐿1, 𝐿2, 𝐿3, 𝐿4} with two variables as shown in the figure below. The initial estimated solution is 𝑋0. Solve the system with two different orders: (a) 𝐿1 → 𝐿2 → 𝐿3 → 𝐿4 and (b) 𝐿1 → 𝐿3 → 𝐿2 → 𝐿4 , respectively. Compare their performance in terms of convergence rate.

Relevant Equations

In the picture below

My answer:
The ART algorithm is a row-action algorithm.
I tried to draw it, but I am not sure whether it will answer the question

 

[Baluncore]

I don't think you have answered the question.

An interesting method.
I would expect the rate of convergence to be proportional to the product of the line slopes. But that is independent of the order.

ART = Algebraic Reconstruction Technique
https://en.wikipedia.org/wiki/Algebraic_reconstruction_technique
https://en.wikipedia.org/wiki/Kaczmarz_method