I have a problem where I am trying to solve many systems of equations, that have very few variables per equation, but a lot of equations. For example potentially 10 variables max in a single equation, but a million equations. A lot of them are trivial in finding a solution, but some of the larger equations are difficult to solve.
I have a naive algorithm in mind to simply solve the trivial equations first, and hope those solutions can then just translate into solving more and more etc, until the more complicated problems are completely solved. Is this a solid initial approach? Is there a different way of thinking about this type of problem that I do not know about? I have tried looking through this SE and similar but I tend to get confused once people start mentioning sparse matrices verse dense ones and things such as that. If someone could point me in the right direction that would be awesome.