Inversion and pseudoinversion of block arrowhead matrices

摘要

One important application of the Sherman–Morrison formula is the construction of an efficient method for computing the inverse of an arrowhead matrix. Our intention is to apply the Sherman–Morrison–Woodbury formula in finding new representations for numeric or symbolic computation of the inverse of block arrowhead matrices. In addition, a generalization of the well known notion of the Schur complement is defined and exploited. Finally, we present a new representation for numeric and symbolic computing of the Moore–Penrose inverse of special type of block arrowhead matrices. Estimated computational complexity as well as presented numerical and symbolic results show the effectiveness of the proposed methods.