Recursive Solution of Certain Structured Linear Systems
André Klein, Peter Spreij · SIAM Journal on Matrix Analysis and Applications · 2007
We provide explicit representations of the null space $\mathcal{S}$ of adjoints of companion-related matrices and of certain rectangular generalized Vandermonde matrices of block Toeplitz type which are encountered in the Fisher information matrix of time series processes. A formula for the right-inverse of this class of matrices A is provided which allows one to express the solution of the system $Ax=b$ as $x=A^{-}b+$ $\mathcal{S}$. The formulas can be easily turned into solution algorithms.