Patterns that preserve sparsity in orthogonal factorization

AbstractAn m × n zero-nonzero pattern A with the Hall property allows a full rank matrix A ϵ A with a QR factorization. The union of patterns occurring in Q over all such A is denoted by Q. By further restricting A to have the strong Hall property, a Hasse diagram that is a forest is used to characterize patterns A that yield Q = A, thus preserving the sparsity of A. For fixed n, the sparsest n × n such patterns are characterized by a binary rooted tree