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A systolic array provides an alternative computing paradigm to the von Neuman architecture. Though its hardware implementation has failed as a paradigm to design integrated circuits in the past, we are now discovering that the systolic array as a software virtualization layer can lead to an extremely scalable execution paradigm. To demonstrate this scalability, in this paper, we design and implement a 3D virtual systolic array to compute a tile QR decomposition of a tall-and-skinny densedoi:10.1142/s0129626414420043 fatcat:tug2bdpfnnd5fcei4qmz2nqdye