Algorithm-based fault tolerance for matrix inversion with maximum pivoting

[[abstract]]Existing fault-tolerant matrix-inversion schemes suffer several drawbacks, such as being limited to fault detection, requiring rollback to resume computation, cost ineffectiveness, instability, significant roundoff errors, and potential false alarms. In this paper, an algorithm-based fault-tolerant scheme for matrix inversion with maximum pivoting that can rectify the above problems is presented. This scheme can correct a single fault and detect multiple faults in each row and column in each iteration within a computation. The sequential and parallel algorithms based on checksums to support the fault-tolerant capability are developed. In this scheme, redundant processing elements needed and additional overhead for the enhanced fault correcting ability are relatively small compared to those in existing schemes. An implementation example that performs n ? n matrix inversion with maximum pivoting on an (n + 1) ? (n + 1) mesh-connected array processor with a time complexity of O(n2) is also described.