Solving general sparse linear systems with LU factorization and graph coloring

Posted on February 1, 2016October 19, 2016 by OrangeOwl

The fast solution of sparse linear systems is a very critical problem in many applications. As of November 2015, the cuSPARSE library offers routines for the solution of sparse linear systems based on LU decomposition, in particular cusparse<t>csrilu02 and cusparse<t>csrsv2_solve Furthermore, cuSPARSE offers the cusparse<t>csrcolor which implements graph coloring. The use of graph coloring for incomplete LU-factorization is described in Graph Coloring: More Paral...

Solving sparse positive definite linear systems by Cholesky factorization

Posted on January 11, 2016October 19, 2016 by OrangeOwl

On our Git Hub website, we have added a fully worked example on how using LU factorization to solve sparse linear systems.

Solving tridiagonal linear systems in CUDA

Posted on January 11, 2016October 19, 2016 by OrangeOwl

Tridiagonal linear systems can be easily solved in the framework of the cuSPARSE library by aid of the function: cusparse<t>gtsv() cuSPARSE also provides cusparse<t>gtsv_nopivot() which, at variance with the first mentioned routine, does not perform pivoting. Both the above functions solve the same linear system with multiple right hand sides. A batched routine cusparse<t>gtsvStridedBatch() also exists which solves multiple linear systems. For all the above routi...

Solving General Sparse Linear Systems in CUDA

Posted on October 5, 2015October 19, 2016 by OrangeOwl

One possibility to solve general sparse linear systems in CUDA is using cuSOLVER. CuSOLVER has three useful routines: 1. cusolverSpDcsrlsvlu, which works for square linear systems (number of unknowns equal to the number of equations) and internally uses sparse LU factorization with partial pivoting; 2. cusolverSpDcsrlsvqr, which works for square linear systems (number of unknowns equal to the number of equations) and internally uses sparse QR factorization; 3. cusolverSpDcsrlsqvqr, w...