  This paper is devoted to condition numbers of the total least squares problem
with linear equality constraint (TLSE). With novel limit techniques, closed
formulae for normwise, mixed and componentwise condition numbers of the TLSE
problem are derived. Computable expressions and upper bounds for these
condition numbers are also given to avoid the costly Kronecker product-based
operations. The results unify the ones for the TLS problem. For TLSE problems
with equilibratory input data, numerical experiments illustrate that normwise
condition number-based estimate is sharp to evaluate the forward error of the
solution, while for sparse and badly scaled matrices, mixed and componentwise
condition numbers-based estimates are much tighter.
