Comments on ‘Simplification of Large Linear Systems using A Two-Step Iterative Method’: A Two-Step Projection Algorithm

✍ Scribed by F.F. Shoji

• Publisher: Elsevier Science
• Year: 1982
• Tongue: English
• Weight: 238 KB
• Volume: 313
• Category: Article
• ISSN: 0016-0032
• DOI: 10.1016/0016-0032(82)90002-3

✦ Synopsis

This brief communication establishes a two-step iterative algorithm based on theorthogonalprojection forreducing orderof the high-ordersystem transferfunction orstate variableequations. A two-step iterativealgorithm which has been developed by the authors (1) consists of the residue and pole (or eigenvalue) optimization with respect to the objective function. Here, the optimum residues in thefirst step can be determined by using the reciprocal basis in the projection theorem. The reciprocal basis allows one to avoid performing the Grammian inversion. Selecting the new basis, the optimum poles in the second step can be also applied for the orthogonal projection. Although the resulting reduced-order models derived from this geometrical point of view

are consistent with models of a two-step iterative algorithm, the algorithm is thus a computationally much simpler way to derive the formula. I. Introducfion 4'0 = a(). Now, let y. and f. be transformed as Yoi Yo(O = Y(t) -(Yo+o, 1 jr,; 90(t) = EC0 -~0403 then y. and jr, belong to the function space of 268 (8) (9) the finite energy L2(T);