SOLUTION OF LINEAR-SYSTEMS OF EQUATIONS IN THE PRESENCE OF 2 TRANSIENT HARDWARE FAULTS

An algorithmic fault tolerant scheme in presented for the solution via LU decomposition of a linear system of equations in the presence of u p to two transient hardware faults. In the general case, where the fau lts affect arbitrary entries in the coefficient matrix array, the meth ods are based on an application of the extended Euclidean algorithm sc heme for decoding BCH and RS codes. In the special case, where the fau lts are assumed not to affect (distinct) entries in the same row of th e array, a simplified algorithm is given with a corresponding reductio n in the hardware overhead. After detection, location and correction o f the fault-induced errors, the Sherman-Morrison-Woodbury formula is u sed to determine the correct solution vector of the linear system, wit hout requiring a valid triangular decomposition of the coefficient mat rix.