| 1. |
- Fanizza, Giovanna, et al.
(författare)
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Passivity-preserving model reduction by analytic interpolation
- 2007
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Ingår i: Linear Algebra and its Applications. - : Elsevier BV. - 0024-3795 .- 1873-1856. ; 425:2-3, s. 608-633
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Tidskriftsartikel (refereegranskat)abstract
- Antoulas and Sorensen have recently proposed a passivity-preserving model-reduction method of linear systems based on Krylov projections. The idea is to approximate a positive-real rational transfer function with one of lower degree. The method is based on an observation by Antoulas (in the single-input/single-output case) that if the approximant is preserving a subset of the spectral zeros and takes the same values as the original transfer function in the mirror points of the preserved spectral zeros, then the approximant is also positive real. However, this turns out to be a special solution in the theory of analytic interpolation with degree constraint developed by Byrnes, Georgiou and Lindquist, namely the maximum-entropy (central) solution. By tuning the interpolation points and the spectral zeros, as prescribed by this theory, one is able to obtain considerably better reduced-order models. We also show that, in the multi-input/multi-output case, Sorensen's algorithm actually amounts to tangential Nevanlinna-Pick interpolation.
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| 2. |
- Jarlebring, Elias, et al.
(författare)
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Polynomial two-parameter eigenvalue problems and matrix pencil methods for stability of delay-differential equations
- 2009
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Ingår i: Linear Algebra and its Applications. - : Elsevier BV. - 0024-3795 .- 1873-1856. ; 431:3-4, s. 369-380
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Tidskriftsartikel (refereegranskat)abstract
- Several recent methods used to analyze asymptotic stability of delay-differential equations (DDEs) involve determining the eigenvalues of a matrix, a matrix pencil or a matrix polynomial constructed by Kronecker products. Despite some similarities between the different types of these so-called matrix pencil methods, the general ideas used as well as the proofs differ considerably. Moreover, the available theory hardly reveals the relations between the different methods. In this work, a different derivation of various matrix pencil methods is presented using a unifying framework of a new type of eigenvalue problem: the polynomial two-parameter eigenvalue problem, of which the quadratic two-parameter eigenvalue problem is a special case. This framework makes it possible to establish relations between various seemingly different methods and provides further insight in the theory of matrix pencil methods. We also recognize a few new matrix pencil variants to determine DDE stability. Finally, the recognition of the new types of eigenvalue problem opens a door to efficient computation of DDE stability. (C) 2009 Elsevier Inc. All rights reserved.
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| 3. |
- Tkachev, Vladimir
(författare)
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Ullemar's formula for the moment map, II
- 2005
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Ingår i: Linear Algebra and its Applications. - : Elsevier BV. - 0024-3795 .- 1873-1856. ; 404:1-3, s. 380-388
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Tidskriftsartikel (refereegranskat)abstract
- We prove the complex analogue of Ullemar's formula for the Jacobian of the complex moment mapping. This formula was previously established in the real case.
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| 4. |
- Nahtman, Tatjana
(författare)
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Marginal permutation invariant covariance matrices with applications to linear models
- 2006
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Ingår i: Linear Algebra and its Applications. - Stockholm : Statistiska institutionen. - 0024-3795. ; 417:1
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Tidskriftsartikel (refereegranskat)abstract
- Abstract.The goal of the present paper is to perform a comprehensive study of the covariance structures in balanced linear models containing random factors which are invariant with respect to marginal permutations of the random factors. We shall focus on model formulation and interpretation rather than the estimation of parameters. It is proven that permutation invariance implies a specific structure for the covariance matrices.Useful results are obtained for the spectra of permutation invariant covariance matrices. In particular, the reparameterization of random effects, i.e., imposing certain constraints, will be considered. There are many possibilities to choose reparameterization constraints in a linear model, however not every reparameterization keeps permutation invariance. The question is if there are natural restrictions on the random effects in a given model, i.e., such reparameterizations which are defined by the covariance structure of the corresponding factor. Examining relationships between the reparameterization conditions applied to the random factors of the models and the spectrum of the corresponding covariance matrices when permutation invariance is assumed, restrictions on the spectrum of the covariance matrix are obtained which lead to 'sum-to-zero' reparameterization of the corresponding factor.
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| 5. |
- Savas, Berkant
(författare)
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Dimensionality reduction and volume minimization - generalization of the determinant minimization criterion for reduced rank regression problems
- 2006
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Ingår i: Linear Algebra and its Applications. - : Elsevier BV. - 0024-3795. ; 418:1, s. 201-214
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Tidskriftsartikel (refereegranskat)abstract
- In this article we propose a generalization of the determinant minimization criterion. The problem of minimizing the determinant of a matrix expression has implicit assumptions that the objective matrix is always nonsingular. In case of singular objective matrix the determinant would be zero and the minimization problem would be meaningless. To be able to handle all possible cases we generalize the determinant criterion to rank reduction and volume minimization of the objective matrix. The generalized minimization criterion is used to solve the following ordinary reduced rank regression problem: minrank(X)=kdet(B-XA)(B-XA)T, where A and B are known and X is to be determined. This problem is often encountered in the system identification context.
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