Effective retraining "models" in the method of multivariate interpolation

We investigate machine learning method based on the theory of random functions. This paper shows a method of rapid retraining "model" when adding new data to the existing ones. This approach reduces the computational complexity of constructing an updated "model" from $O(m^3)$ to from $O(m^2)$. The term "model" means interpolating or approximating function constructed from the training data. This approach can have an independent value in the area of linear algebra as applied to a well-conditioned linear systems with symmetric matrix.