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- Zhaojun Bai, Daniel Skoogh
- 2003

A Krylov subspace based projection method is presented for model reduction of large scale bilinear systems. A reduced bilinear system is constructed in such a way that it matches a desired number of moments of multivariable transfer functions corresponding to the kernels of Volterra series representation of the original system. Applications to the… (More)

- Zhaojun Bai, Daniel Skoogh
- 2002

Means of applying Krylov subspace techniques for adaptively extracting accurate reduced-order models of large-scale nonlinear dynamical systems is a relatively open problem. There has been much current interest in developing such techniques. We focus on a bi-linearization method, which extends Krylov subspace techniques for linear systems. In this approach,… (More)

Rational Krylov is an extension of the Lanczos or Arnoldi eigenvalue algorithm where several shifts (matrix factorizations) are performed in one run. A variant has been developed, where these factoriza-tions are performed in parallel. It is shown how Rational Krylov can be used to nd a reduced order model of a large linear dynamical system. In Electrical… (More)

- Daniel Skoogh
- 1998

An algorithm to compute a reduced-order model of a linear dynamic system is described. It is based on the rational Krylov method, which is an extension of the shift-and-invert Arnoldi method where several shifts (interpolation points) are used to compute an orthonormal basis for a sub-space. It is discussed how to generate a reduced-order model of a linear… (More)

Avhandling ffr teknologie doktorsexamen i numerisk analys vid Chalmers Tekniska HHgskola. Abstract New variants of Krylov subspace methods for numerical solution of linear systems, eigenvalue, and model order reduction problems are described. A new method to solve linear systems of equations with several right-hand sides is described. It uses the basis from… (More)

An implementation of a parallel rational Krylov method for the gen-eralised matrix eigenvalue problem is discussed. The implementation has been done on a MIMD computer and a cluster of workstations. The rational Krylov algorithm is an extension of the shift-and-invert Arnoldi method where several shifts are used to compute basis vectors for one subspace. In… (More)

- Daniel Skoogh
- 1998

A new method to solve linear systems of equations with several right-hand sides is described. It uses the basis from a previous solution to reduce the number of matrix vector products needed to solve a linear system of equations with a new right-hand side. It builds up a subspace of a union of Krylov spaces. Some numerical examples are given where variants… (More)

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