Inversion of generalized Cauchy matrices and other classes of structured matrices

Fast inversion algorithms for strongly nonsingular matrices of the form \(C = \left[ {\frac{{z_i^T{y_j}}}{{{c_i} - {d_j}}}} \right]\) (generalized Cauchy matrices), where z i , y j are column vectors and c i , d j are complex numbers, are presented. The approach is based on the interpretation of equations Cξ = η as tangential interpolation problems. Furthermore, it is described how other types of structured matrices like Toeplitz matrices and their generalizations can be transformed into generalized Cauchy matrices. This transformation can be utilized in order to get stable algorithms.

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