3) up to a certain tolerance can be understood as performing instead of an exact matrix-vector multiplication Hv, an inexact matrix-vector multiplication given by

The benchmarks achieved included distributing control algorithms on up to eight cores simultaneously and performing a 3,000-by-6,000 matrix-vector multiplication within 0.

In the tight-binding code, the matrix-vector multiplication is time-consuming, but the dominant time cost is still the vector reorthogonalization in the Arnoldi solver.

3 we test how many eigenvalues can we extract with a limited number of matrix-vector multiplications, i.

We ran algorithm G2 endowed with algorithm 3 of the previous section for matrix-vector multiplication on a cluster of parallel computers with MPI communication protocol.

A new H-matrix arithmetic has been developed which allows (approximate) matrix-vector multiplication and matrix-matrix operations such as addition, multiplication, LU-factorization and inversion of matrices in this format.

The probing method approximates a matrix using only matrix-vector multiplication.

The natural parallel algorithm for sparse matrix-vector multiplication with an arbitrary distribution of matrix and vectors consists of the following four phases: