# Computing entries of a matrix in parallel using GPU

I am trying to solve $Ax=b$ a system of linear equation. The matrix $A=(a_{ij})$ is constructed as $$a_{ij}=\int_0^1\int_0^1 K(x,y)h_i(x)h_j(y) dxdy.$$ The evaluation of integral takes a lot of time, and overall computation is very slow. Can I evaluate these integrals in parallel using GPU cores? Please suggest how can I compute these integrals simultaneously??

thanks

• Probably, although the operation is non-local and therefore data-transfer might be a bottle-neck that limits the obtainable speed-up. What you are computing is called a Fredholm integral operator, so googling "Fredholm GPU" seems to give some useful hits (e.g., Johan Nordström's Bachelor thesis). You should also take a look at Andreas Klöckner's webpage. – Christian Clason Jul 11 '15 at 9:13
• This question is way to broad. Start by writing C code, then optimize it, then thread it. If you know that your bottleneck at that point is ameliorated by GPU hardware, then consider an OpenCL port – Jeff Jul 18 '15 at 15:36