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We present a set of new batched CUDA kernels for the LU factorization of a large collection of independent problems of different size, and the subsequent triangular solves. All kernels heavily exploit the registers of the graphics processing unit (GPU) in order to deliver high performance for small problems. The development of these kernels is motivated by the need for tackling this embarrasingly-parallel...
Many problems in engineering and scientific computing require the solution of a large number of small systems of linear equations. Due to their high processing power, Graphics Processing Units became an attractive target for this class of problems, and routines based on the LU and the QR factorization have been provided by NVIDIA in the cuBLAS library. This work addresses the situation where the systems...
This paper compares different Krylov methods based on short recurrences with respect to their efficiency whenimplemented on GPUs. The comparison includes BiCGSTAB, CGS, QMR, and IDR using different shadow space dimensions. These methods are known for their good convergencecharacteristics. For a large set of test matrices taken from theUniversity of Florida Matrix Collection, we evaluate the methods'performance...
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