TP Model Transformation Via Sequentially Truncated Higher-Order Singular Value Decomposition

The sequentially truncated higher-order singular value decomposition (ST-HOSVD) is applied to a tensor product (TP) model transformation instead of the compact form of HOSVD (CHOSVD). The goal is to reduce computational cost in the transformation. By using the ST-HOSVD, the TP model transformations of systems and the related algorithms are executed and the ST-HOSVD based canonical form and the weighting functions are given. To see the effectiveness, we take a dynamic system and TORA system as numerical examples. A great reduction of complexity is seen in use of the ST-HOSVD compared with use of the CHOSVD in TP model transformation. The approximation of the new method seems as good as the original one.