Chapter 22. Sparse Matrix-Vector Multiplication

By Gordon Fossum

This chapter describes an optimized implementation of the Sparse Matrix-Vector Multiplication (SpMV) algorithm using OpenCL.

Sparse matrices, for the purposes of this chapter, are defined as large two-dimensional matrices in which the vast majority of the elements of the matrix are equal to zero. They may be largely diagonal, or not. They may be symmetric, or not (perhaps not even square). They may be singular (containing entire rows with no non-zero elements), or not. They are used to characterize and solve problems in a wide variety of domains.

The sample uses a new portable tiled and packetized sparse matrix data format, which has both a single-precision and a double-precision ...

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