Contragredient Transformations Applied to the Optimal Projection Equations
1992) Contragredient Transformations Applied to the Optimal Projection Equations. Technical Report TR-92-28, Computer Science, Virginia Polytechnic Institute and State University. (
The optimal projection approach to solving the H2 reduced order model problem produces two coupled, highly nonlinear matrix equations with rank conditions as constraints. It is not obvious from their original form how they can be differentiated and how some algorithm for solving nonlinear equations can be applied to them. A contragredient transformation, a transformation which simultaneously diagonalizes two symmetric positive semi-definite matrices, is used to transform the equations into forms suitable for algorithms for solving nonlinear problems. Three different forms of the equations obtained using contragredient transformations are given. An SVD-based algorithm for the contragredient transformation and a homotopy algorithm for the transformed equations are given, together with a numerical example.
|Item Type:||Departmental Technical Report|
|Subjects:||Computer Science > Historical Collection(Till Dec 2001)|
|Deposited By:||User autouser|
|Deposited On:||05 December 2001|