Structured matrices and inverses
For researchers and practitioners working with structured matrices, this extends the known property of structured inverses to more general inverses, though the result is incremental.
The paper shows that several types of inverses of structured matrices (with small displacement rank), including the Moore-Penrose inverse of rank-deficient matrices, are also structured, enabling fast inversion and reduced storage.
A matrix (and any associated linear system) will be referred to as structured if it has a small displacement rank. It is known that the inverse of a structured matrix is structured, which allows fast inversion (or solution), and reduced storage requirements. According to two definitions of displacement structure of practical interest, it is shown here that several types of inverses are also structured, including the Moore-Penrose inverse of rank-deficient matrices.