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References in periodicals archive ?
The aim of this work is the approximation of the matrix vector product f(A)b without explicitly computing the matrix f(A) by an extrapolation procedure.
Garzan, "A new approach for sparse matrix vector product on NVIDIA GPUs," Concurrency Computation Practice and Experience, vol.
To explain, first it is beneficial to demonstrate full O([N.sup.2.sub.b][M.sup.2.sub.b]) matrix vector product which explicitly loads each matrix element,
Additionally, the multilevel fast multipole algorithm (MLFMA) [15-23] is utilized to accelerate the computations of matrix vector product. Numerical examples have demonstrated the validity and efficiency of the proposed scheme.
The straight forward algorithm for this matrix vector product, which is called NDFT in Algorithm 1, takes O(M [N.sub.[pi]]) arithmetical operations and stores no matrix elements at all, but rather uses M [N.sub.[pi]] direct calls of the function cexp() to evaluate the complex exponentials [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII].
When matrix vector products are expensive relative to other arithmetic operations, smaller matrix vector product usage correlates directly with shorter wall clock times.
Since at each Broyden step, only the vectors z and s from the previous step are required, and the inversion term on the right-hand side of (45) is simply a scalar, the computation of the inverse- matrix vector product is very efficient.
Mrozowski, "A memory efficient and fast sparse matrix vector product on a GPU," Progress In Electromagnetics Research, Vol.
Returning to Algorithm 1, we now consider the situation when for the matrix vector product Hs, we approximate the solution of each of the linear systems in steps 2 and 4.
In Table 5, we report the number of matrix vector products and CPU times for Newton-DACG as compared with "pure" DACG, that is, with DACG run with a final tolerance of [10.sup.-8].
The iterative Krylov subspace solver does not require an expensive decomposition of the system matrix, but instead uses a sequence of matrix vector products to iteratively get a good approximation of the solution of the linear system.
Example A l n nnz b 6.1 ILLC1850 1850 712 8638 ILLC1850-RHS1 6.2 E30R0000 9661 9661 305794 E30R0000-RHS1 6.3 LANDMARK 71952 2704 1146848 rand(71952,1) 6.4 BIG_DUAL 30269 30269 89858 Axrand(30269,1) TABLE 6.2 Number of matrix vector products with A and [A.sup.T] required to get [parallel][A.sup.T] r[parallel]/[parallel] [A.sup.T] [r.sub.0][parallel] [less than or equal to] [10.sup.-12] using different values of j in the gap strategy given in Section 2.