  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 functions 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.

Numerical Analysis;Numerical Analysis