On the Equivalent of Structure Preserving Reductions Approach and Adjoint Networks Approach for VLSI Interconnect Reductions

Two versions of Krylov subspace order reduction techniques for VLSI interconnect reductions, including structure preserving reductions approach and adjoint networks approach, will be comparatively investigated. Also, we will propose a modified structure preserving reduction algorithm to speed up the projection construction in a linear order. The numerical experiment shows the high accuracy and low computational consumption of the modified method. In addition, it will be shown that the projection subspace generated from the structure-preserving approach and those from the adjoint networks approach are equivalent. Therefore, transfer functions of both reduced networks are identical.