Fault-tolerant high-performance matrix multiplication: theory and practice

We extend the theory and practice regarding algorithmic fault-tolerant matrix-matrix multiplication, C=AB, in a number of ways. First, we propose low-overhead methods for detecting errors introduced not only in C but also in A and/or B. Second, we show that, theoretically, these methods will detect all errors as long as only one entry, is corrupted. Third we propose a low-overhead roll-back approach to correct errors once detected. Finally, we give a high-performance implementation of matrix-matrix multiplication that incorporates these error detection and correction methods. Empirical results demonstrate that these methods work well in practice while imposing an acceptable level of overhead relative to high-performance implementations without fault-tolerance.