Displacement structure of weighted pseudoinverses
It is known that if the rank of a matrix displacement is small then fast algorithms for this matrix are available. The paper deals with the estimates for the rank of \(A^+_{M,N} V - U A^+_{M,N}\)-type displacements, that provide some extensions of known results on Sylvester and Stein UV-displacements. Here \(A^+_{M,N}\) denotes the weighted Moore-Penrose inverse of \(A\), where \(M\) and \(N\) are square Hermitian positive definite complex matrices. The above results are applied then to obtain the corresponding bounds for some generalizations of Toeplitz, Vandermonde, and Cauchy matrices.
scientific article; zbMATH DE number 2082052