Mixed-Precision analysis of Householder QR Algorithms
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Although mixed precision arithmetic has recently garnered interest for training dense neural networks, many other applications could benefit from the speed-ups and lower storage if applied appropriately. The growing interest in employing mixed precision computations motivates the need for rounding error analysis that properly handles behavior from mixed precision arithmetic. We present a framework for mixed precision analysis that builds on the foundations of rounding error analysis presented in [Higham, Nicholas, "Accuracy and Stability of Numerical Algorithms", SIAM] and demonstrate its practicality by applying the analysis to various Householder QR Algorithms. In addition, we present successful results from using mixed precision QR factorization for some small-scale benchmark problems in graph clustering.
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