A fast sparse block circulant matrix vector product

In the context of computed tomography (CT), iterative image reconstruction techniques are gaining attention because high-quality images are becoming computationally feasible. They involve the solution of large systems of equations, whose cost is dominated by the sparse matrix vector product (SpMV). Our work considers the case of the sparse matrices being block circulant, which arises when taking advantage of the rotational symmetry in the tomographic system. Besides the straightforward storage saving, we exploit the circulant structure to rewrite the poor-performance SpMVs into a high-performance product between sparse and dense matrices. This paper describes the implementations developed for multi-core CPUs and GPUs, and presents experimental results with typical CT matrices. The presented approach is up to ten times faster than without exploiting the circulant structure.Romero Alcalde, E.; Tomás Domínguez, AE.; Soriano Asensi, A.; Blanquer Espert, I. (2014). 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Performance Optimization and Modeling of Blocked Sparse Kernels

International audienceWe present a method for automatically selecting optimal implementations of sparse matrix-vector operations. Our software “AcCELS” (Accelerated Compress-storage Elements for Linear Solvers) involves a setup phase that probes machine characteristics, and a run-time phase where stored characteristics are combined with a measure of the actual sparse matrix to find the optimal kernel implementation. We present a performance model that is shown to be accurate over a large range of matrices