# Solving general sparse linear systems with LU factorization and graph coloring

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...
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# Solving sparse positive definite linear systems by Cholesky factorization

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

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...
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# Solving General Sparse Linear Systems in CUDA

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...
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