In gradient descent for collaborative filtering, are x and theta update simultaneous?

Question

I'm taking Andrew Ng's machine learning course and I'm on chapter 16: Recommender Systems. I currently finished watching the part about collaborative filtering. In it, he talked about how you can guess the parameters: theta, then use it to predict x and use the predicted x to learn better parameters, and so on. He also said it could be done simultaneously and gave the gradient descent algorithm for it:

I want to ask if x and theta are updated simultaneously. Eg, for each iteration: after performing a single gradient descent on x, do i recalculate the square error sum using the new values of x and then perform a gradient descent on theta then repeat until convergence. OR do i perform a single gradient descent on x, using the same squared error sum, perform a gradient descent on theta too

Answer 1

You can do it in one update simultaneously. You could even summarize it in one formular updating x and theta at the same time using: