## A parallel multithreaded sparse triangular linear system solver.(English)Zbl 1453.65059

Summary: We propose a parallel sparse triangular linear system solver based on the Spike algorithm. Sparse triangular systems are required to be solved in many applications. Often, they are a bottleneck due to their inherently sequential nature. Furthermore, typically many successive systems with the same coefficient matrix and with different right hand side vectors are required to be solved. The proposed solver decouples the problem at the cost of extra arithmetic operations as in the banded case. Compared to the banded case, there are extra savings due to the sparsity of the triangular coefficient matrix. We show the parallel performance of the proposed solver against the state-of-the-art parallel sparse triangular solver in Intel’s Math Kernel Library (MKL) on a multicore architecture. We also show the effect of various sparse matrix reordering schemes. Numerical results show that the proposed solver outperforms MKL’s solver in $$\sim 80\%$$ of cases by a factor of 2.47, on average.

### MSC:

 65F05 Direct numerical methods for linear systems and matrix inversion 65Y05 Parallel numerical computation
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