In this paper we derive a direct method for block tridiagonalizing a single-input single-output system triple {A, b, c}. The method is connected to the nonsymmetric Lanczos procedure developed in [10, 2, 1] and also l...
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In this paper we derive a direct method for block tridiagonalizing a single-input single-output system triple {A, b, c}. The method is connected to the nonsymmetric Lanczos procedure developed in [10, 2, 1] and also leads to canonical representations of such triples.
numerical calculations for a time-accurate solution of the equations of fluid dynamics often require a time-step constraint. One can reduce this constraint to an inequality relating the time step, the grid spacing, an...
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numerical calculations for a time-accurate solution of the equations of fluid dynamics often require a time-step constraint. One can reduce this constraint to an inequality relating the time step, the grid spacing, and some reference wave velocity. Historically, the literature in numerical analysis refers to this parametric cluster as the Courant number (nondimensional) and the condition for the linear case as the Courant-Friedrichs-Lewy (CFL) condition. Classically, numerical analysis relies on linearization and von Neumann's use of Fourier series to derive the CFL condition. In practice, computational fluid dynamics mostly relies on rules of thumb and heuristic arguments to justify the equation that determines time-step size and numerical stability for complicated and nonlinear calculations. The approach proposed in this paper uses the second law of thermodynamics as a way of imposing a restriction on the time step, applied to linear and nonlinear equations and systems of equations like the equations of gas dynamics. Basically, by transforming the truncation error for the numerical formula approximating a conservation equation into an equation representing the balance of entropy, one can obtain an inequality that restricts the time step to satisfy the second law. The second law as developed extends its role by analogy for the simple linear advection equation, then a nonlinear equation, and finally a system of equations representing the one-dimensional equations of gas dynamics. In each case results obtained agree with the classical approach for linear equations but differ in others, indicating that the second law has significant implications beyond its role in thermodynamics. This work develops the topic only for explicit numerical algorithms with truncation errors no greater than second order. By conjecture one expects that the most general conclusions will field for implicit and higher-order methods because of the universality of the second law and the concept o
An algorithm for shape offsetting is presented that is based on level-set propagation. This algorithm avoids the topological problems encountered in traditional offsetting algorithms, and it deals with curvature singu...
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An algorithm for shape offsetting is presented that is based on level-set propagation. This algorithm avoids the topological problems encountered in traditional offsetting algorithms, and it deals with curvature singularities by including an 'entropy condition' in its numerical implementation.
A block Toeplitz algorithm is proposed to perform the J-spectral factorization of a para-Hermitian polynomial matrix. The input matrix can be singular or indefinite, and it can have zeros along the imaginary axis. The...
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A block Toeplitz algorithm is proposed to perform the J-spectral factorization of a para-Hermitian polynomial matrix. The input matrix can be singular or indefinite, and it can have zeros along the imaginary axis. The key assumption is that the finite zeros of the input polynomial matrix are given as input data. The algorithm is based on numerically reliable operations only, namely computation of the null-spaces of related block Toeplitz matrices, polynomial matrix factor extraction and linear polynomial matrix equations solving. (c) 2006 Elsevier Ltd. All rights reserved.
In this paper, we introduce a novel algorithm for calculating arbitrary order cumulants of multidimensional data. Since the dth order cumulant can be presented in the form of a d-dimensional tensor, the algorithm is p...
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In this paper, we introduce a novel algorithm for calculating arbitrary order cumulants of multidimensional data. Since the dth order cumulant can be presented in the form of a d-dimensional tensor, the algorithm is presented using tensor operations. The algorithm provided in the paper takes advantage of supersymmetry of cumulant and moment tensors. We show that the proposed algorithm considerably reduces the computational complexity and the computational memory requirement of cumulant calculation as compared with existing algorithms. For the sizes of interest, the reduction is of the order of d! compared to the naive algorithm.
Using appropriate similarity transform, we present the partial differential equation formulation of both floating strike and fixed strike American lookback option models. We examine the early exercise policies of the ...
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Using appropriate similarity transform, we present the partial differential equation formulation of both floating strike and fixed strike American lookback option models. We examine the early exercise policies of the floating strike and fixed strike American lookback options, while the realized extrmum of the asset price can be monitored continuously or discretely, The characterizations of the optimal exercise prices of American lookback options are also discussed. For the numerical valuation of the American lookback options, several approaches for deriving efficient and accurate numerical results are addressed.
It is briefly reminded how the theory of dual plastic potentials has been used in the past to generate analytical expressions for plastic potentials of anisotropic polycrystalline materials with a known crystallograph...
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It is briefly reminded how the theory of dual plastic potentials has been used in the past to generate analytical expressions for plastic potentials of anisotropic polycrystalline materials with a known crystallographic texture. Such constitutive models are fairly general, and the identification of their parameters can readily be done on the basis of data obtained from a texture measurement. As a result, they are suitable for engineering applications such as elasticplastic finite element models for forming processes. However, the yield loci generated in this way are not automatically convex. Therefore, a new variant of the method has now been developed, which preserves the advantages of the old method, but for which convexity can at least been tested by means of a mathematical criterion. In addition, it has turned out to be possible to slightly modify plastic potentials which do not satisfy the criterion, in order to achieve convexity. An example of a plastic potential modified in this way is discussed. After modification, it was still a good analytical approximation of the plastic potential directly derived from the Taylor-Bishop-Hill theory on the basis of the crystallographic texture of the material. (C) 2003 Elsevier Ltd. All rights reserved.
The present simulations of jets illustrate the effects of sub-grid modelingbased on eddy viscosity in LES. The effective flow Reynolds number is found to be dramaticallydecreased using the dynamic Smagorinsky model, w...
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The present simulations of jets illustrate the effects of sub-grid modelingbased on eddy viscosity in LES. The effective flow Reynolds number is found to be dramaticallydecreased using the dynamic Smagorinsky model, whereas it seems to be preserved and to correspond tothe initial jet conditions using the selective filtering alone, This basic deficiency of theeddy-viscosity subgrid modeling can question its use for the study of free shear flows where theReynolds number is a key parameter, as for instance for the investigation of jet noise.
A study considers the fundamental problem of circular orbit phasing by performing a multiple-impulse maneuver. It is shown below that the peculiar properties of the considered problem allow a simpler procedure of find...
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A study considers the fundamental problem of circular orbit phasing by performing a multiple-impulse maneuver. It is shown below that the peculiar properties of the considered problem allow a simpler procedure of finding the globally optimal solution. It appears to be composed of two- and four-impulse maneuvers and switches between them as the phasing maneuver duration grows. Two-impulse maneuvers do not require any optimization, as they are unambiguously calculated as least-delta-v solutions to the multiple-revolution Lambert problem.
A different approach to the solution of a nonlinear set of algebraic equations is presented. It is basically a revision of the Newton iterative algorithm from a digital control point of view, The Newton algorithm is c...
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A different approach to the solution of a nonlinear set of algebraic equations is presented. It is basically a revision of the Newton iterative algorithm from a digital control point of view, The Newton algorithm is considered like a digital control algorithm that acts on a set of nonlinear algebraic equations. Its target is to find a value x* that satisfies the algebraic equation set. This value can be considered as a particular ''input'' of the equation set which gives a zero ''output'' while the iteration index can be considered as the clock of the digital system. From this point of view some correlations between the stability of digital systems and the Newton algorithm can be shown, This approach allows us to understand the reasons behind the convergence failure of some modified Newton algorithms such as source stepping, damping, and limiting that literature often reports as heuristic.
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