SPARSE MATRIX–VECTOR MULTIPLICATION
This chapter introduces irregular algorithms and presents the example of multiplying a sparse matrix with a vector, which is the central operation in iterative solvers for linear systems and eigensystems. The irregular sparsity pattern of the matrix does not change during the multiplication, and the multiplication may be repeated many times with the same matrix. This justifies putting a lot of effort in finding good data distribution for a parallel multiplication. A useful non-Cartesian matrix distribution called the Mondriaan distribution is introduced, and an algorithm for finding such a distribution for a general sparse matrix is studied. Several special types of matrices are analyzed, such as random sparse matrices and Laplacian matrices. The program of this chapter demonstrates the use of the bulk synchronous message passing primitives from BSPlib, which were designed to facilitate irregular computations.
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