A Highly Efficient Implementation of Multiple Precision Sparse Matrix-Vector Multiplication and Its Application to Product-type Krylov Subspace Methods [article]

Tomonori Kouya
2014 arXiv   pre-print
We evaluate the performance of the Krylov subspace method by using highly efficient multiple precision sparse matrix-vector multiplication (SpMV). BNCpack is our multiple precision numerical computation library based on MPFR/GMP, which is one of the most efficient arbitrary precision floating-point arithmetic libraries. However, it does not include functions that can manipulate multiple precision sparse matrices. Therefore, by using benchmark tests, we show that SpMV implemented in these
more » ... ns can be more efficient. Finally, we also show that product-type Krylov subspace methods such as BiCG and GPBiCG in which we have embedded SpMV, can efficiently solve large-scale linear systems of equations provided in the UF sparse matrix collections in a memory-restricted computing environment.
arXiv:1411.2377v1 fatcat:mld2ljfc4ndjdf5rupyycd4l2i