Department of Mathematics, Tel Aviv University and University of Maryland
icg@math.umd.eduFast inversion algorithms for structured matrices usually do not allow pivoting and assume that the principal minors of the matrix are invertible. Recently was developed the "look ahead" approach which enables these restrictions to be avoided. Here an alternative method is proposed which is based on fast algorithms of Gaussian elimination for structured matrices. These algorithms use pivoting for Cauchy matrices. For Toeplitz matrices various formulas which transform them in matrices of Cauchy type are proposed. Discrete Fourier Transform and displacement structure of matrices play an important role.