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Tensor decompositions are a powerful technique for enabling comprehensive and complete analysis of real-world data. Data analysis through tensor decompositions involves intensive computations over large-scale irregular sparse data. Optimizing the execution of such data intensive computations is key to reducing the time-to-solution (or response time) in real-world data analysis applications. As high-performance...
Tensor analysis (through tensor decompositions) is increasingly becoming popular as a powerful technique for enabling comprehensive and complete analysis of real-world data. In many critical modern applications, large-scale tensor data arrives continuously (in streams) or changes dynamically over time. Tensor decompositions over static snapshots of tensor data become prohibitively expensive due to...
We present the sparse multidimensional FFT (sMFFT) for positive real vectors with application to image processing. Our algorithm works in any fixed dimension, requires an (almost)-optimal number of samples (O (Rlog (N over R))) and runs in O (Rlog (N over R)) complexity (to first order) for N unknowns and R nonzeros. It is stable to noise and exhibits an exponentially small probability of failure...
Writing high performance software requires the programmer to take advantage of multi-core processing. This can be done through tools like OpenMP, which allow the programmer to mark parallel loops. Identifying parallelizable loops, however, is a non-trivial task. Furthermore, transformations can be applied to a loop nest to expose parallelism. Polyhedral compilation has become an increasingly popular...
Existing high-level, source-to-source compilers can accept input programs in a high-level language (e.g., C) and perform complex automatic parallelization and other mappings using various optimizations. These optimizations often require trade-offs and can benefit from the user's involvement in the process. However, because of the inherent complexity, the barrier to entry for new users of these high-level...
As distributed memory systems grow larger, communication demands have increased. Unfortunately, while the costs of arithmetic operations continue to decrease rapidly, communication costs have not. As a result, there has been a growing interest in communication-avoiding algorithms for some of the classic problems in numerical computing, including communication-avoiding Fast Fourier Transforms (FFTs)...
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