How to update ARX model with new sample data without re-calculating it fully?

I found some aproaches in literature, but all of them claim that i need to rewrite arx() function, what i do not want to do.

UPD: i was asked to give more detail, well:

Initially I have a dataset of N inputs and 1 output, i build ARX model using ARX function - so i obtain coefficients for inputs and previous outputs to get value of current output - exactly as described here: https://www.mathworks.com/help/ident/ref/arx.html

Then my program gets new samples of data (for example if initial model was built on 10k measurements - i get 100 new rows) and i do not want to recalculate model on 10100 rows (initial 10k rows are not to be stored) - what i want to do is correct coefficients i have, according to newly obtained data. In literature i found some examples of doing that - but it is quite complicated for realization, so, I wonder if Matlab provides any option for solving this problem.

Feel free to ask for another details. Thank you in advance!

[Birdman]

Give more detail.