Hi, this actually helped a lot and made good sense. The differential equation I'm working with do include a set of singular matrices and with the application of a higher order time integration method, I do end up with a matrix A that is badly conditioned. Computing the condition number in Julia cond(A) yields an enormous result (it is nearly too embarrasing to state actually - I get 4.8e11). Computing det(A) gave me Inf too. I guess I've been too naive to think I could reuse old code for lower order time integration methods, which gave me quite good results, still with a relatively high condition number (1.6e10)?
Seems like my next step now, would be to "unravel" my matrix A. Den torsdag den 11. august 2016 kl. 14.47.24 UTC+2 skrev Tamas Papp: > > 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 > >> > >
