Representation of quasiseparable matrices using excluded sums and equivalent charges

A new parametric representation for the general quasiseparable matrix is derived, based on the ideas from the multipole method. It uses functional expansions and successive skeleton approximations, approximations, but finally is formulated in the matrix language. The number of parameters is linear in the dimension of the matrix and in the quasiseparable rank. Stable numerical algorithm is provided for the computation of parameters, defining the decomposition. Numerical examples illustrate the effectiveness of our approach.