Formulation of Matrix Pade Approximation in Rectangular Full Packed Storage

The Extended Euclidean algorithm for matrix Pade approximants is applied to compute matrix Pade approximants in rectangular full packed format (RFP) if the coefficient matrices of the input matrix polynomial are triangular. The procedure given by Gustavson et al for packing a triangular matrix in rectangular full packed format is applied to pack sequence of lower triangular matrices of a matrix polynomial in Rectangular Full Packed format. This RFP format of a matrix polynomial is applied to compute matrix Pade approximants of the matrix polynomial using Matrix Pade Extended Euclidean Algorithm. Algorithms for the multiplication of two triangular matrices and inverse of a triangular matrix in RFP format are also presented. The CPU time and memory comparison in computing the matrix Pade approximants of a matrix polynomial between RFP format case and non packed case are elucidated in detail.