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Recursive low rank Hankel approximation and model reduction.
Get PDFIn this note we present a new updating technique to
estimate a low rank approximation of the Hankel map
of a time-varying system. We obtain error estimates
of our approximation and also explain how to use this
for model reduction of time-varying as well as time
invariant systems
Optimal Preconditioning for Mixed Finite Element Formulation of Second-Order Elliptic Problems
Get PDFOptimal Preconditioning for Raviart-Thomas Mixed Formulation of Second-Order Elliptic Problems
No full textSet-theoretical solutions to the Yang-Baxter Relation from factorization of matrix polynomials and theta functions
Get PDFNew set-theoretical solutions to the Yang—Baxter Relation are constructed. These solutions arise from the decompositions ``in different order'' of matrix polynomials and θ-functions. We also construct a ``local action of the symmetric group'' in these cases, generalizations of the action of the symmetric group SN given by the set-theoretical solution
Design of experiments in the presence of errors in factor levels
Get PDFThis paper is concerned with the statistical properties of experimental designs where the factor levels cannot be set precisely. When the errors in setting the factor levels cannot be measured, design robustness is explored. However, when the actual design could be measured at the end of the investigation, its optimality is of interest. D-optimality could be assessed in different ways. Several measures are compared. Evaluating them is difficult even in simple cases. Therefore, in general, simulations are used to obtain their values. It is shown that if D-optimality is measured by the expected value of the determinant of the information matrix of the experimental design, as has been suggested in the past, on average the designs appear to improve with the variance of the error in setting the factor levels. However, we argue that the criterion of D-optimality should be based on the inverse of the information matrix. In this case it is shown that the experiment could be better or worse than the planned one. It is also recognized that setting the factor levels with error could lead to an increased risk of losing observations, which on its own could reduce considerably the optimality of the experimental designs. Advice on choosing the design region in such a way that such a risk is controlled to an acceptable level is given
Adjoint Formulations in Impedance Imaging
Get PDFMost reconstruction algorithms in electrical impedance tomography (EIT, ERT and ECT) are known to
suffer from the computational costs of calculating the Jacobian (also known as sensitivity matrix). In
this paper we review and slightly modify the adjoint fields technique already widely used in
electromagnetic imaging, diffuse optical and ultrasound tomography, which enables the reconstruction
of nonlinear solutions without the explicit calculation of the Jacobian. This has enormous
computational advantages in the efficiency of image reconstruction. Here we address the complex
isotropic EIT problem
Solving the indefinite least squares problem by hyperbolic QR factorization
Get PDFThe indefinite least squares (ILS) problem involves minimizing a certain type of indefinite quadratic form. We develop perturbation theory for the problem and identify a condition number. We describe and analyze a method for solving the ILS problem based on hyperbolic QR factorization. This method has a lower operation count than one recently proposed by Chandrasekaran, Gu, and Sayed that employs both QR and Cholesky factorizations. We give a rounding error analysis of the new method and use the perturbation theory to show that under a reasonable assumption the method is forward stable. Our analysis is quite general and sheds some light on the stability properties of hyperbolic transformations. In our numerical experiments the new method is just as accurate as the method of Chandrasekaran, Gu, and Sayed
Confidence characteristics of distributions
No full textWe introduce the confidence characteristic of a distribution as the distribution corresponding to the decomposition concentration function. We show that the decomposition concentration function has very good differentiability properties for any distribution, that the Lebesgue measures of the shortest confidence regions of a distribution and its confidence characteristic are the same, and that similar properties hold for the entropies and the level sets of their densities
High order effects in one-step reaction-sheet jump conditions for premixed flames
No full textThe differences need to be understood between the leading order jump conditions, often assumed at a flame sheet in combustion theory, and the actual effect of a one step chemical reaction governed by Arrhenius kinetics. These differences are higher order in terms of a large activation temperature analysis and can be estimated using an asymptotic approach. This paper derives one order of asymptotic correction to the leading order jump conditions that are normally used for describing premixed laminar combustion, providing additional contributions that are due to curvature, flow through the flame sheet and the temperature gradient into the burnt gas. As well as offering more accurate asymptotic results, these can be used to estimate the errors that are inherent in adopting only the leading order version and they can point towards major qualitative changes that can occur at finite activation temperatures in some cases. Applied to steady non-adiabatic flame balls it is found that the effect of a non-zero temperature gradient in the burnt gas provokes the most serious deficiency in the asymptotic approach
Splitting for dissipative particle dynamics
Get PDFWe study numerical methods for dissipative particle dynamics, a system of stochastic differential equations for simulating particles interacting pairwise according to a soft potential at constant temperature where the total momentum is conserved. We introduce splitting methods and examine the behavior of these methods experimentally. The performance of the methods, particularly temperature control, is compared to the modified velocity Verlet method used in many previous papers