We derive a recursive algorithm for the time-update of the triangular factors of non-Hermitian time-variant matrices with structure. These are matrices that undergo low-rank modifications as time progresses. special cases of which often arise in adaptive filtering and instrumental variable (IV) methods. A natural implementation of the algorithm is via two coupled triangular arrays of processing elements. We consider, in particular, an IV parameter estimation problem and show how the arrays collapse to a coupled parallelizable solution of the identification problem.