In the case of the 1D methodology (methods 1 to 4), and for data matrices of size (F·T ×K, it is necessary to compute transformation matrices of size (F·F)×n, while for the 2D methodology (methods 5 to 8), two transformation matrices of F×n r and T×n c are needed while working with two data matrices of size T×(F·K) and F×(T·K).
This method is based on a Hadamard matrix of size N×N and a pair of Hadamard matrices of size M×M.
The synthesis metrics related to the implementation of the systolic arrays architectures as coprocessors are summarized in Table 3. First, we exemplify the MSF, PSM and iterative POCS coprocessor architectures for the following simplified specifications: data matrices of size and two Band-Toeplitz PSF matrices of the same pixel size with equal bandwidths of 2 and 2 pixels.
As a starting point, consider an input matrix (X) of size m × n, where 'm' is the number of features and 'n' is the number of samples, and a very small number 'k' called 'low-rank.' Typically, k ≪ min(m,n) may be in the order of 50's for matrix in size of millions, while k less than 10 is typical for matrices of size in a few thousands.
Moreover, the per-RB-based processing nature of the polynomial interpolation method may lead to computational savings since for N total subcarriers and N ′ subcarriers per RB, the LMMSE method requires inversion of complex-valued matrices of size (frac {N}{N'}L), while the polynomial interpolators require inversion of real-valued Vandermonde matrices of size p where (p
For example, matrices of size (mxn) will be generated if row_numbers[i] == m and col_numbers[i] == n for some i.
The identification of the solution involves matrices of size (3 × 3) computed off-line.
The explicit polynomial that we consider is the iterated matrix multiplication polynomial of n generic matrices of size n×n.
Furthering these developments, we present GPU design and optimization techniques for high-performance batched one-sided factorizations of millions of tiny matrices (of size 32 and less).
We show experimental results on matrices of size up to the order of one billion with nearly perfect scaling by using up to 1024 MPI processes.
On a K40c GPU for contractions resulting in GEMMs on square matrices of size 8 for example, we are 2.8× faster than CUBLAS, and 8.5× faster than MKL on 16 cores of Intel Xeon E5-2670 (Sandy Bridge) 2.60GHz CPUs.
