SVD‐Krylov–Based Structure‐Preserving Techniques for Approximation of a Class of Second‐Order Index‐1 Descriptor Systems

This work is aimed at deriving a computationally efficient approach to approximate the second‐order Index‐1 descriptor systems without exploiting the fundamental structure of the systems, which ensures both the accuracy of the approximation and the feasibility of computation time. It demonstrates the structure‐preserving iterative singular‐value decomposition (SVD)‐Krylov algorithm (ISKA) which is a hybrid two‐sided projections strategy combined with a computationally feasible Krylov subspace technique and the stability‐preserving iterative technique based SVD. ISKA is a model‐order reduction (MOR) approach utilized to get a reduced‐order model (ROM) corresponding to a target model with a desired size, where two projector matrices are the main constituent. The left projector matrix will be constructed using the low‐rank Cholesky‐factor alternative direction implicit (LRCF‐ADI) technique, whereas the right projector matrix will be constructed utilizing the well‐known Krylov subspace. The main focus of this work is to avoid the so‐called first‐order conversion of the second‐order systems and ensure the invariance of the matrix‐vector operations of the original systems. A real‐world model derived from the adaptive spindle support system will be utilized as the target model to numerically validate the competency and efficiency of the proposed strategy through MATLAB simulations. Accuracy of the approximation, stability of the ROMs, and optimization of computational time are the prime concerns of this work. To confirm the advancement of the proposed approach, it will be compared with the existing approaches employing the necessary figures and tables.