On design of wavefront-driven algorithms for processing large-scale band-limited matrices on rotary arrays

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Abstract A design of wavefront-driven algorithms is presented for processing matrix operations associated with solving large-scale band-limited dense matrix equations, Ax = b. The design provides a guide-line for specifying the functionality of each processing element PE, array arrangements of PEs, communication structures and parallel algorithms. The basic feature of the design is (it1) a rotary array arrangement of data-flow type PEs with the slant width 2B+1 and the circumference Z= about 2B on which the diagonal strip of a band- limited matrix data is wound around (B = the half band width of the matrix A), and (2) pipelined executions of tasks, each of which consists of a group of pipelined wavefronts and circulates around the rotary array. For the matrix equations solver, a wavefront algorithm is proposed that first produces the Gaussian solution via LU decomposition. Accuracy is improved by applying the residual iteration, preconditioned by a truncated inverse U-*L-*.

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