Displaying similar documents to “Reduction of large circuit models via low rank approximate gramians”

Efficient numerical algorithms for balanced stochastic truncation

Peter Benner, Enrique Quintana-Ortí, Gregorio Quintana-Ortí (2001)

International Journal of Applied Mathematics and Computer Science

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We propose an efficient numerical algorithm for relative error model reduction based on balanced stochastic truncation. The method uses full-rank factors of the Gramians to be balanced versus each other and exploits the fact that for large-scale systems these Gramians are often of low numerical rank. We use the easy-to-parallelize sign function method as the major computational tool in determining these full-rank factors and demonstrate the numerical performance of the suggested implementation...

Extracting second-order structures from single-input state-space models: Application to model order reduction

Jérôme Guillet, Benjamin Mourllion, Abderazik Birouche, Michel Basset (2011)

International Journal of Applied Mathematics and Computer Science

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This paper focuses on the model order reduction problem of second-order form models. The aim is to provide a reduction procedure which guarantees the preservation of the physical structural conditions of second-order form models. To solve this problem, a new approach has been developed to transform a second-order form model from a state-space realization which ensures the preservation of the structural conditions. This new approach is designed for controllable single-input state-space...

Inversion of square matrices in processors with limited calculation abillities

Krzysztof Janiszowski (2003)

International Journal of Applied Mathematics and Computer Science

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An iterative inversion algorithm for a class of square matrices is derived and tested. The inverted matrix can be defined over both real and complex fields. This algorithm is based only on the operations of addition and multiplication. The numerics of the algorithm can cope with a short number representation and therefore can be very useful in the case of processors with limited possibilities, like different neuro-computers and accelerator cards. The quality of inversion can be traced...

A parallel block Lanczos algorithm and its implementation for the evaluation of some eigenvalues of large sparse symmetric matrices on multicomputers

Mario Guarracino, Francesca Perla, Paolo Zanetti (2006)

International Journal of Applied Mathematics and Computer Science

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In the present work we describe HPEC (High Performance Eigenvalues Computation), a parallel software package for the evaluation of some eigenvalues of a large sparse symmetric matrix. It implements an efficient and portable Block Lanczos algorithm for distributed memory multicomputers. HPEC is based on basic linear algebra operations for sparse and dense matrices, some of which have been derived by ScaLAPACK library modules. Numerical experiments have been carried out to evaluate HPEC...

On the choice of subspace for iterative methods for linear discrete ill-posed problems

Daniela Calvetti, Bryan Lewis, Lothar Reichel (2001)

International Journal of Applied Mathematics and Computer Science

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Many iterative methods for the solution of linear discrete ill-posed problems with a large matrix require the computed approximate solutions to be orthogonal to the null space of the matrix. We show that when the desired solution is not smooth, it may be possible to determine meaningful approximate solutions with less computational work by not imposing this orthogonality condition.