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Full-Text Articles in Mathematics
A Proper Orthogonal Decomposition Approach To Approximate Balanced Truncation Of Infinite Dimensional Linear Systems, John R. Singler, Belinda A. Batten
A Proper Orthogonal Decomposition Approach To Approximate Balanced Truncation Of Infinite Dimensional Linear Systems, John R. Singler, Belinda A. Batten
Mathematics and Statistics Faculty Research & Creative Works
We extend a method for approximate balanced reduced order model derivation for finite dimensional linear systems developed by Rowley (Int. J. Bifur. Chaos Appl. Sci. Eng. 15(3) (2005), pp. 997-1013) to infinite dimensional systems. The algorithm is related to standard balanced truncation, but includes aspects of the proper orthogonal decomposition in its computational approach. The method can be also applied to nonlinear systems. Numerical results are presented for a convection diffusion system.
Approximate Low Rank Solutions Of Lyapunov Equations Via Proper Orthogonal Decomposition, John R. Singler
Approximate Low Rank Solutions Of Lyapunov Equations Via Proper Orthogonal Decomposition, John R. Singler
Mathematics and Statistics Faculty Research & Creative Works
We present an algorithm to approximate the solution Z of a stable Lyapunov equation AZ + ZA* + BB* = 0 using proper orthogonal decomposition (POD). This algorithm is applicable to large-scale problems and certain infinite dimensional problems as long as the rank of B is relatively small. In the infinite dimensional case, the algorithm does not require matrix approximations of the operators A and B. POD is used in a systematic way to provide convergence theory and simple a priori error bounds.
Balanced Proper Orthogonal Decomposition For Model Reduction Of Infinite Dimensional Linear Systems, John R. Singler, Belinda A. Batten
Balanced Proper Orthogonal Decomposition For Model Reduction Of Infinite Dimensional Linear Systems, John R. Singler, Belinda A. Batten
Mathematics and Statistics Faculty Research & Creative Works
In this paper, we extend a method for reduced order model derivation for finite dimensional systems developed by Rowley to infinite dimensional systems. The method is related to standard balanced truncation, but includes aspects of the proper orthogonal decomposition in its computational approach. The method is also applicable to nonlinear systems. The method is applied to a convection diffusion equation.