The Kronecker structure of [mathematical expression not reproducible] inherited by the low operator TT rank of A allows for efficient
matrix-vector multiplications despite the fact that this matrix is not sparse.
Then the
matrix-vector multiplication of [mathematical expression not reproducible] can be written as
It is well known that the
matrix-vector multiplication [F.sub.2K][[mu].sub.2K] can be carried out in 0(2K log 2K) = 0(K log K) operations via the fast Fourier transform.
The size of the matrices being multiplied and of the vector in case of
matrix-vector multiplication is determined from the loop iteration limits.
AlMazroo, "FPGA design and implementation of dense
matrix-vector multiplication for image processing application," in Proceedings of the World Congress of Engineering and Computer Science (WCECS '10), vol.
In the tight-binding code, the
matrix-vector multiplication is important, but the dominant part of the CPU time is the vector reorthogonalization in the Arnoldi solver, which is parallelized efficiently by PARPACK.
For example, a matrix multiplication in APL is obtained by combining the operators "+", ".", and "x", whereas in MATLAB the operator "*" is overloaded to perform all linear algebra multiplications, such as inner product, outer product,
matrix-vector multiplication, and matrix multiplication.
MARKOVIC, A scalable sparse
matrix-vector multiplication kernel for energy-efficient sparse-BLAS on FPGAs, in Proceedings of the 2014 ACM/SIGDA International Symposium on Field-programmable Gate Arrays, FPGA '14, ACM, New York, 2014, pp.
Then, we apply FFT instead of
matrix-vector multiplication directly to enhance efficiency in inner product computation in (25).
which means that only a single
matrix-vector multiplication is needed to obtain E or [??] once F is available.
For instance, on most architectures, the
matrix-vector multiplication benchmark will be dominated by the time for broadcast (SPREAD) and reduction (SUM).
The multilevel fast multipole algorithm is a powerful tool for accelerating the
matrix-vector multiplication and it is shown to have ability to solve electrically large and complex problems [5-7].
