Mathematical derivation of alternating Least squares (ASL)

Recently in the CF related papers, "collaborative Filtering for implicit Feedback Datasets" thought very well, very easy to understand, but from the objective function

How to derive the formula for the renewal of Xu and Yi is not well described, so write it down
Derivation:
The first derivative of Xu:

Where Y is the item matrix, n*f, each line is a item_vec,c^u is a diagonal matrix of n*n dimension,
Each element on the diagonal is c_ui,p (u) is a n*1 column vector, and its element i is p_ui.
Then the derivative = 0, which can be:

Since X_u and y_i are symmetric in the objective function, it is easy to get:

where x is the user matrix, the M*f dimension, each line is a user_vec,c^i is the diagonal matrix of m*m, each element on the diagonal is c_ui,p (i) is the m*1 column vector, its first and the element is p_ui
Then the derivative = 0, which can be:

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Mathematical derivation of alternating Least squares (ASL)