I'm interested in determining the precision of the matrix solution using matlabs "x = A\b" solver.
The "A" I am working with is a non-singular, symmetric n x n matrix (that is typically 100x100, but I am interested in the general case). Elements in this matrix are either 0 or some number between 10^-8 and 10^-4. There are typically around 7n non-zero elements (3n in upper diagonal, 3n in lower diagonal, all diagonal elements are non-zero).
The "b" I am working with is a vector of length n with all elements zero except one or two elements which are numbers between -5 and 5 (of some arbitrary order of magnitude).
Does anyone have any ideas of where I can look or a method that I could use to calculate this?
I haven't been able to find the details of what is behind the hood of the default MATLAB solver