Reprocessing a Postprocessed Elimination Tree to Obtain Exact Sparsity Prediction in Qr Factorization

Row-merge trees for forming the QR factorization of a sparse matrix A are closely related to elimination trees for the Cholesky factorization of ATA. Row-merge trees predict the exact fill-in (assuming no numerical cancellation) provided A satisfies the strong Hall property, but over-estimates the fill-in in general. However, here a fast and simple post-processing step for rowmerge trees is presented that predicts the exact fill-in for sparse QR factorization using Householder reflectors, for general matrices.