The impact of vector and parallel architectures on the Gaussian elimination algorithm
The impact of vector and parallel architectures on the Gaussian elimination algorithm
LAPACK Users' guide (third ed.)
LAPACK Users' guide (third ed.)
OpenMP: An Industry-Standard API for Shared-Memory Programming
IEEE Computational Science & Engineering
Understanding the efficiency of GPU algorithms for matrix-matrix multiplication
Proceedings of the ACM SIGGRAPH/EUROGRAPHICS conference on Graphics hardware
LU-GPU: Efficient Algorithms for Solving Dense Linear Systems on Graphics Hardware
SC '05 Proceedings of the 2005 ACM/IEEE conference on Supercomputing
Journal of VLSI Signal Processing Systems
Benchmarking GPUs to tune dense linear algebra
Proceedings of the 2008 ACM/IEEE conference on Supercomputing
International Journal of High Performance Computing Applications
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Dense matrix inversion is a basic procedure in many linear algebra algorithms. A computationally arduous step in most dense matrix inversion methods is the inversion of triangular matrices as produced by factorization methods such as LU decomposition. In this paper, we demonstrate how triangular matrix inversion (TMI) can be accelerated considerably by using commercial Graphics Processing Units (GPU) in a standard PC. Our implementation is based on a divide and conquer type recursive TMI algorithm, efficiently adapted to the GPU architecture. Our implementation obtains a speedup of 34x versus a CPU-based LAPACK reference routine, and runs at up to 54 gigaflops/s on a GTX 280 in double precision. Limitations of the algorithm are discussed, and strategies to cope with them are introduced. In addition, we show how inversion of an L- and U-matrix can be performed concurrently on a GTX 295 based dual-GPU system at up to 90 gigaflops/s.