Algorithm-Based Fault Tolerance in Linear Algebra Tasks

The modification of weighted checksum method is proposed, which allows to derive the fault tolerant versions of most linear algebra algorithms. The purpose is detection and correction of calculation errors occurred due to transient hardware faults. Using the proposed method, the fault-tolerant version of Faddeeva algorithm is designed in this paper. The computational complexity of new algorithm is increased approximately on O(N) multiply-add operations in comparison with the original one. However, new algorithm enables to detect and to correct a single error in an arbitrary row or column of input data matrices at the each algorithm step. Finally, the results of experimental verification of the proposed algorithm are represented.