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roughly, in a regression context, non linear least square is a problem set-up ; for a starter, see

http://en.wikipedia.org/wiki/Non-linear_least_squares

http://en.wikipedia.org/wiki/Least_squares#Differences_between_linear_and_non-linear_least_squares

.

alternating least square is a method (among many others) to find an appropriate factorization of a large matrix, when the objective function is given in least square sense ; see ALS for PCA computation in the link below :

http://columbiadatascience.com/2012/10/18/week-7-hunch-com-recommendation-engines-svd-alternating-least-squares-convexity-filter-bubbles/

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