I don't know anything about your problem domain, but are you sure that the errors are not a conditioning problem? Increasing precision can mitigate this to a limited extent, but when you increase the dimension you quickly run out of precision, so it is rarely the solution. Have you checked the singular values of A? (Sorry if you already did this as the first thing, just thought I would ask).
On Thu, Aug 11 2016, Nicklas Andersen wrote: > I know I might be contradicting myself by saying *"I would like not to > introduce too much error by the use of an iterative solver"* and then going > on with propagating errors, direct solvers and a wish for quadruple > precision. > In theory direct solvers give an exact solution, while iterative give an > approximation. In this case, when doing the further analysis it would be a > lot easier for me, to just argue for a direct solver than an iterative > solver. > I hope you somehow get what I'm trying to say. > > Thank you again :) > > Den torsdag den 11. august 2016 kl. 14.04.40 UTC+2 skrev Nicklas Andersen: >> >> Hey again. >> >> Thank you all for the nice answers. I was in a bit of hurry and didn't >> have time to go into too much detail, so to clarify: >> The system I'm trying to solve arises from the space dicretization of a >> *linear* partial differential algebraic equation. >> To advance the solution in time I need to solve a system Ax=b at each time >> step. >> Large is a bit loosely formulated, since the system more or less only has >> size around 500x500 to 2000x2000, but it needs to be solved, lets say, at >> most 640 times. >> I would prefer a direct solver since I need the results for an analysis of >> the time integration method and would like not to introduce too much error >> by the use of an iterative solver. >> That said, speed is not my nr. 1 priority, but it would be nice. >> >> The reason I need quadruple precision is that it seems like some >> components introduce round off error and these errors propagate, such that >> I in the end get negative convergence of my method. >> >> Regard Nicklas >>
