Matrix computations (3rd ed.)
Solution of the matrix equation AX + XB = C [F4]
Communications of the ACM
FLAME: Formal Linear Algebra Methods Environment
ACM Transactions on Mathematical Software (TOMS)
State-space truncation methods for parallel model reduction of large-scale systems
Parallel Computing - Special issue: Parallel and distributed scientific and engineering computing
The science of deriving dense linear algebra algorithms
ACM Transactions on Mathematical Software (TOMS)
Approximation of Large-Scale Dynamical Systems (Advances in Design and Control) (Advances in Design and Control)
Families of algorithms related to the inversion of a Symmetric Positive Definite matrix
ACM Transactions on Mathematical Software (TOMS)
Solving linear-quadratic optimal control problems on parallel computers
Optimization Methods & Software
Parallel algorithms for balanced truncation model reduction of sparse systems
PARA'04 Proceedings of the 7th international conference on Applied Parallel Computing: state of the Art in Scientific Computing
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We propose an efficient implementation of the Balanced Truncation (BT) method for model order reduction when the state-space matrix is symmetric (positive definite). Most of the computational effort required by this method is due to the computation of matrix inverses. Two alternatives for the inversion of a symmetric positive definite matrix on multi-core platforms are studied and evaluated, the traditional approach based on the Cholesky factorization and the Gauss-Jordan elimination algorithm. Implementations of both methods have been developed and tested. Numerical experiments show the efficiency attained by the proposed implementations on the target architecture.