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Numerical computation of an analytic singular value decomposition of a matrix valued function
This paper extends the singular value decomposition to a path of matricesE(t). An analytic singular value decomposition of a path of matricesE(t) is an analytic path of factorizationsE(t)=X(t)S(t)Y(t) T whereX(t) andY(t) are orthogonal andS(t) is diagonal. To maintain differentiability the diagonal entries ofS(t) are allowed to be either positive or negative and to appear in any order. This paper investigates existence and uniqueness of analytic SVD's and develops an algorithm for computing them. We show that a real analytic pathE(t) always admits a real analytic SVD, a full-rank, smooth pathE(t) with distinct singular values admits a smooth SVD. We derive a differential equation for the left factor, develop Euler-like and extrapolated Euler-like numerical methods for approximating an analytic SVD and prove that the Euler-like method converges
Interleukin-8 and eicosanoid production in the lung during moderate to severe Pneumocystis carinii pneumonia in AIDS: a role of interleukin-8 in the pathogenesis of P. carinii pneumonia
The type III effectors HsvG and HsvB of gall-forming Pantoea agglomerans determine host specificity and function as transcriptional activators
Conservation of a Resistance Gene-like Fragment ADG2 Related to Patato Y Potyvirus Resistance Gene Ryadg in Diploid and Tetrasomic Tetraploid Potato Lines
Model order reduction : methods, concepts and properties
This chapter offers an introduction to Model Order Reduction (MOR). It gives an overview on the methods that are mostly used. It also describes the main concepts behind the methods and the properties that are aimed to be preserved. The sections are in a prefered order for reading, but can be read independentlty. Section 4.1, written by Michael Striebel, E. Jan W. ter Maten, Kasra Mohaghegh and Roland Pulch, overviews the basic material for MOR and its use in circuit simulation. Issues like Stability, Passivity, Structure preservation, Realizability are discussed. Projection based MOR methods include Krylov-space methods (like PRIMA and SPRIM) and POD-methods. Truncation based MOR includes Balanced Truncation, Poor Man’s TBR and Modal Truncation.Section 4.2, written by Joost Rommes and Nelson Martins, focuses on Modal Truncation. Here eigenvalues are the starting point. The eigenvalue problems related to large-scale dynamical systems are usually too large to be solved completely. The algorithms described in this section are efficient and effective methods for the computation of a few specific dominant eigenvalues of these large-scale systems. It is shown how these algorithms can be used for computing reduced-order models with modal approximation and Krylov-based methods.Section 4.3, written by Maryam Saadvandi and Joost Rommes, concerns passivity preserving model order reduction using the spectral zero method. It detailedly discusses two algorithms, one by Antoulas and one by Sorenson. These two approaches are based on a projection method by selecting spectral zeros of the original transfer function to produce a reduced transfer function that has the specified roots as its spectral zeros. The reduced model preserves passivity.Section 4.4, written by Roxana Ionutiu, Joost Rommes and Athanasios C. Antoulas, refines the spectral zero MOR method to dominant spectral zeros. The new model reduction method for circuit simulation preserves passivity by interpolating dominant spectral zeros. These are computed as poles of an associated Hamiltonian system, using an iterative solver: the subspace accelerated dominant pole algorithm (SADPA). Based on a dominance criterion, SADPA finds relevant spectral zeros and the associated invariant subspaces, which are used to construct the passivity preserving projection. RLC netlist equivalents for the reduced models are provided.Section 4.5, written by Roxana Ionutiu and Joost Rommes, deals with synthesis of a reduced model: reformulate it as a netlist for a circuit. A framework for model reduction and synthesis is presented, which greatly enlarges the options for the re-use of reduced order models in circuit simulation by simulators of choice. Especially when model reduction exploits structure preservation, we show that using the model as a current-driven element is possible, and allows for synthesis without controlled sources. Two synthesis techniques are considered: (1) by means of realizing the reduced transfer function into a netlist and (2) by unstamping the reduced system matrices into a circuit representation. The presented framework serves as a basis for reduction of large parasitic R/RC/RCL networks