a library that is part of the NVIDIA CUDA toolkit to accelerate various dense and sparse LAPACK-like operations on GPUs
cusolver is a library included with CUDA 7.0 and beyond, to provide GPU acceleration for 3 categories of linear algebra problems:
cuSolverDN deals with dense matrix factorization and solve routines such as LU, QR, SVD and LDLT
cuSolverSP provides a set of sparse routines based on a sparse QR factorization
cuSolverRF is a sparse re-factorization package for solving a sequence of matrices where only the coefficients are changed but the sparsity pattern remains the same
cusolver documentation is here.