topic solving sparse systems of linear equations in Intel® oneAPI Math Kernel Library

solving sparse systems of linear equations

stansy — Sat, 15 Sep 2012 21:54:43 GMT

Hi,

I tried to use DSS to solve systems of linear equations in the optimization process. Unfortunately, my sparse matrix is ill-defined for the calculations and the result is erroneous results. Is it possible to use Intel MKL to solve this problem?

Enclosed is a simple example that explains my problem. Note:onlydiagonalelements arechanged duringoptimization.

Regards,

Stan

Hi,

Alexander_K_Intel2 — Wed, 19 Sep 2012 10:57:51 GMT

Hi, Matrix from your example correspond grid version of operator of 4th derivatives with Neumann boundary condition so it's has at least 2 vectors in Kernel space. This vector correlate const and linear function (x_1 = (1,1,1,1,1,....) and x_2 = (1,2,3,4,5,6,....)). System Ax=b with symmetric degenerate matrix have a solution if and only if rhs vector orthogonal kernel space. Moreover in such case the solution is not unique. In your example b is a part of kernel space so there is not any algebraic solution of you system. With best regards, Alexander Kalinkin

Hi,

stansy — Wed, 19 Sep 2012 16:30:12 GMT

Hi, Alexander, thank you very much for an interesting answer. As I pointed, the calculations (optimization process) are determined diagonal elements of the matrix. I used an the iterative sparse solvers based on the reverse communication interface RCI CG and calculations give good results. Unfortunately, the number of iterations must be very large (about 2000) and my calculations are performed slower than MATLAB. With greetings Stan