Fault tolerant QR-decomposition algorithm and its parallel implementation
A fault tolerant algorithm based on Givens rotations and a modified weighted checksum method is proposed for the QR-decomposition of matrices. The algorithm enables us to correct a single error in each row or column of an input M × N matrix A occurred at any among N steps of the algorithm. This effect is obtained at the cost of 2.5N 2+O(N) multiply-add operations (M=N). A parallel version of the proposed algorithm is designed, dedicated for a fixed-size linear processor array with fully local communications and low I/O requirements.
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