This article presents the first of its kind, in-depth survey covering over two hundred state-of-the-art optimization schemes for solving sparse iterative linear systems with a focus on computing SpMV. Unleashing the full potential of an architecture/accelerator requires determining the factors that affect an efficient implementation of SpMV. Efficient implementation of sparse matrix-vector multiplication (SpMV) and linear solvers are therefore essential and has been subjected to extensive research across a variety of computing architectures and accelerators such as central processing units (CPUs), graphical processing units (GPUs), many integrated cores (MICs), and field programmable gate arrays (FPGAs). The crucial computing kernel for such iterative solutions is the multiplication of a sparse matrix by a dense vector. Iterative solutions of sparse linear systems and sparse eigenvalue problems have a fundamental role in vital fields of scientific research and engineering.
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