Solution of linear systems of equations in the presence of two transient hardware faults

An algorithmic fault tolerant scheme is presented for the solution via LU decomposition of a linear system of equations in the presence of up to two transient hardware faults. In the general case, where the faults affect arbitrary entries in the coefficient matrix array, the methods are based on an application of the extended Euclidean algorithm scheme for decoding BCH and RS codes. In the special case, where the faults are assumed not to affect (distinct) entries in the same row of the array, a simplified algorithm is given with a corresponding reduction in the hardware overhead. After detection, location and correction of the fault-induced errors, the Sherman-Morrison-Woodbury formula is used to determine the correct solution vector of the linear system, without requiring a valid triangular decomposition of the coefficient matrix.