A modified nonsymmetric rational block Lanczos method for model reduction in large scale LTI dynamical systems

We propose an adaptive model reduction algorithm for computing a reduced-order model of dynamical multi-input and multi-output (MIMO) linear time independent (LTI) dynamical systems. The process is based on multipoint moment matching. Moreover, we develop new simple Lanczos-like equations for the rational block case, and we use them to derive simple residual error expressions. An adaptive method for choosing the interpolation points is also proposed. Finally, some numerical experiments are reported to show the effectiveness of the new adaptive modified rational block Lanczos ($\mathtt{AMRBL}$) process when applied to stable linear LTI dynamical systems.