  We present new algorithms to detect and correct errors in the lower-upper
factorization of a matrix, or the triangular linear system solution, over an
arbitrary field. Our main algorithms do not require any additional information
or encoding other than the original inputs and the erroneous output. Their
running time is softly linear in the dimension times the number of errors when
there are few errors, smoothly growing to the cost of fast matrix
multiplication as the number of errors increases. We also present applications
to general linear system solving.
