Fault tolerant matrix triangularization and solution of linear systems of equations

The authors present a fault tolerant algorithm for the solution of linear systems of equations using matrix triangularization procedures suitable for implementation on array architectures. Gaussian elimination with partial or pairwise pivoting and QR decomposition are made fault tolerant against two transient errors occurring during the triangularization procedure. The extended Euclidean algorithm is implemented to solve for the locations and values of the errors defined appropriately using the theory of error correcting codes. The Sherman-Morrison Woodbury formula is then used to obtain the correct solution vector to the linear system of equations without requiring a valid decomposition