Rational interpolation: Modified rational Arnoldi algorithm and Arnoldi-like equations

Krylov projection methods are used for model reduction of large scale systems. An algorithm which belongs to the class of Krylov subspace methods is the Arnoldi algorithm. The standard version of this algorithm tends to create reduced order models that poorly approximate low frequency dynamics. The rational Arnoldi algorithm produces reduced models that approximate dynamics at different interpolation points. This paper tackles the issue of developing a computationally efficient model reduction procedure based on a modified rational Arnoldi algorithm. Moment matching properties are established and a breakdown analysis for the algorithm is provided. A set of Arnoldi-like equations for the algorithm is also derived.