" Newton's Iteration for Inversion of Cauchy-like and Other Structured Matrices "

                            Victor Y. Pan*
              Department of Mathematics and Computer Science
               Lehman College, City University of New York
                         Bronx, NY 10468, USA
                email address: vpan@lcvax.lehman.cuny.edu
                                  and
                    Ph.D. Program in Computer Science
                  Graduate School and University Center
                      City University of New York
              33 West 42nd Street, New York, NY 10036, USA

               Ailong Zheng,   Xiaohan Huang,    Olen Dias
                      Ph.D. Program in Mathematics
                 Graduate School and University Center
                      City University of New York
              33 West 42nd Street, New York, NY 10036, USA

                              < Abstract >
  We specify some initial assumptions that guarantee rapid refinement of a
rough initial approximation to the inverse of a Cauchy-like matrix, by mean
of our new modification of Newton's iteration, where the input, output, and
all the auxiliary matrices are represented with their short generators defined
by the associated scaling operators. The computations are performed fast since
they are confined to operations with short generators of the given and
computed matrices. Because of the known correlations among various structured
matrices, the algorithm is immediately extended to rapid refinement of rough
initial approximations to the inverses of Vandermonde--like,
Chebyshev--Vandermonde--like and Toeplitz--like matrices, where again,
the computations are confined to operations with short generators of the
involved matrices.