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Sparse Matrix-Vector multiplication (SpMV) is an important kernel in many scientific applications and is known to be memory bandwidth limited. On modern processors with wide SIMD and large numbers ...

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Sparse matrix-vector multiplication is an important computational kernel in scientific applications. However, it performs poorly on modern processors because of a low compute-to-memory ratio and its irregular memory access patterns. This paper discusses the implementations of sparse matrix-vector algorithm using OpenMP to execute iterative methods on the Dawning S4800A1.

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You are familier with the fact that matrices and vectors have a kind of "algebra" and that key operations for this algebra are matrix-vector multiplication and matrix-matrix multiplication. When multiplying M*V the rows of the matrix M must have the same number of elements as the vector V, and then the product is defined to be the vector W such ...

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Ii-a Sparse Matrix-Vector Multiplication SpMV can be formally defined as y=Ax, where the input matrix, A (M ×N), is sparse, and the input, x (N ×1), and the output, y (M ×1), vectors are dense. Figure 1 gives a simple example of SpMV with M and N equal to 4, where the number of nonzeros (nnz) of the input matrix is 8.

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Dec 11, 2017 · Clever approach to matrix-vector multiplication A = 0:85 A 1 + 0:15 A 2 Av = (0:85 A 1 + 0:15 A 2)v = 0:85 (A 1 v) + 0:15 (A 2 v) I Multiplying by A 1: use sparse matrix-vector multiplication you implemented in Mat I Multiplying by A 2: Use the fact that A 2 = 2 6 6 6 4 1 1... 1 3 7 7 7 5 1 n 1 1

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pensive. Moreover, since matrix-vector multiplication for sparse matrices is generally limited by memory bandwidth, it is desirable to ﬁnd a storage format for which both Ax and ATx can be computed in parallel without performing more than nnz fetches of nonzeros from the memory to compute either product.