A Symbolic Approach to Compute a Null-Space Basis in the Projection Method

Giesbrecht, Mark; Pham, Nam

doi:10.1007/978-3-662-43799-5_19

Cited by 3 publications

(1 citation statement)

References 13 publications

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“…An appropriate implementation of the proposed procedure is still under investigation. It also might be useful to consider a symbolic computation of the required null spaces, see [7].…”

Section: Remark 5 Inmentioning

confidence: 99%

Structural-algebraic regularization for coupled systems of DAEs

Scholz

Steinbrecher

2015

Bit Numer Math

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In the automated modeling of multi-physics dynamical systems, frequently different subsystems are coupled together via interface or coupling conditions. This approach often results in large-scale high-index differential-algebraic equations (DAEs). Since the direct numerical simulation of these kinds of systems leads to instabilities and possibly non-convergence of numerical methods, a regularization or remodeling of such systems is required. In many simulation environments, a structural method that analyzes the system based on its sparsity pattern is used to determine the index and an index-reduced system model. However, this approach is not reliable for certain problem classes, and in particular not suited for coupled systems of DAEs. We present a new approach for the regularization of coupled dynamical systems that combines the Signature method (Σ-method) for the structural analysis with algebraic regularization techniques. This allows to handle structurally singular systems and also enables a proper treatment of redundancies or inconsistencies in the system.

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“…An appropriate implementation of the proposed procedure is still under investigation. It also might be useful to consider a symbolic computation of the required null spaces, see [7].…”

Section: Remark 5 Inmentioning

confidence: 99%

Structural-algebraic regularization for coupled systems of DAEs

Scholz

Steinbrecher

2015

Bit Numer Math

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A Symbolic-Numerical Approach to Index Reduction and Solution of Differential-Algebraic Equations

Stocco,

Larcher

2025

Lecture Notes in Computer Science

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A Bayesian Covariance Graphical and Latent Position Model for Multivariate Financial Time Series

2017

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Current understanding holds that financial contagion is driven mainly by the systemwide interconnectedness of institutions. A distinction has been made between systematic and idiosyncratic channels of contagion, with shocks transmitted through the latter expected to be substantially more likely to lead to a systemic crisis than through the former. Idiosyncratic connectivity is thought to be driven not simply by obviously shared characteristics among institutions, but more by latent characteristics that lead to the holding of related securities. We develop a graphical model for multivariate financial time series with interest in uncovering the latent positions of nodes in a network intended to capture idiosyncratic relationships. We propose a hierarchical model consisting of a VAR, a covariance graphical model (CGM) and a latent position model (LPM). The VAR enables us to extract useful information on the idiosyncratic components, which are used by the CGM to model the network and the LPM uncovers the spatial position of the nodes. We also develop a Markov chain Monte Carlo algorithm that iterates between sampling parameters of the CGM and the LPM, using samples from the latter to update prior information for covariance graph selection. We show empirically that modeling the idiosyncratic channel of contagion using our approach can relate latent institutional features to systemic vulnerabilities prior to a crisis. . Ahelegbey et al./Bayesian Covariance Graphical And Latent Position Model 3 3.5 Network Density (%) J u n -0 3 J u n -0 4 J u n -0 5 J u n -0 6 J u n -0 7 J u n -0 8 J u n -0 9 J u n -1 0 J u n -1 1 J u n -1 2 J u n -1 3 J u n -1 4 SSSL BSNET(0) BSNET(1) (a) -3 -2 -1 0 1 2 3 4 Standardized Density J u n -0 3 J u n -0 4 J u n -0 5 J u n -0 6 J u n -0 7 J u n -0 8 J u n -0 9 J u n -1 0 J u n -1 1 J u n -1 2 J u n -1 3 J u n -1 4 Procrustes Distance J u n -0 3 J u n -0 4 J u n -0 5 J u n -0 6 J u n -0 7 J u n -0 8 J u n -0 9 J u n -1 0 J u n -1 1 J u n -1 2 J u n -1 3 J u n -1 4Graph Clustering Coefficient J u n -0 3 J u n -0 4 J u n -0 5 J u n -0 6 J u n -0 7 J u n -0 8 J u n -0 9 J u n -1 0 J u n -1 1 J u n -1 2 J u n -1 3 J u n -1 4

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A Symbolic Approach to Compute a Null-Space Basis in the Projection Method

Cited by 3 publications

References 13 publications

Structural-algebraic regularization for coupled systems of DAEs

Structural-algebraic regularization for coupled systems of DAEs

A Symbolic-Numerical Approach to Index Reduction and Solution of Differential-Algebraic Equations

A Bayesian Covariance Graphical and Latent Position Model for Multivariate Financial Time Series

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