In the paper, for systems described by ordinary differential equations a review of algorithms of dynamical input reconstruction by results of inaccurate observations of its solutions is given. The problem under discus...
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In the paper, for systems described by ordinary differential equations a review of algorithms of dynamical input reconstruction by results of inaccurate observations of its solutions is given. The problem under discussion is referred to the class of dynamical inverse problems. The proposed algorithms are stable with respect to informational noises and computational errors. They are based on the combination of methods of the theory of ill-posed problems and the theory of feedback control. The essence of the methodology underlying the algorithms suggested in the paper consists in the representation of a reconstruction algorithm in the form of a feedback control algorithm for a certain artificial dynamical system, a model;such an algorithm, whose output is the realization of the control in the model, is dynamical by its definition.
In this paper we are interested in volume matching C1-splines which, in addition, are positive, monotone, or S-convex. Using particular rational biquadratic splines sufficient conditions are derived in form of linear ...
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In this paper we are interested in volume matching C1-splines which, in addition, are positive, monotone, or S-convex. Using particular rational biquadratic splines sufficient conditions are derived in form of linear equalities and inequalities, and these conditions are shown to be satisfied for sufficiently large rationality parameters.
The effect of rounding errors on an algebraic process is often investigated by means of a so-called backward analysis. In this paper we will discuss the possibility of performing such an analysis on a computer. We beg...
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The effect of rounding errors on an algebraic process is often investigated by means of a so-called backward analysis. In this paper we will discuss the possibility of performing such an analysis on a computer. We begin with a precise definition of a stable algorithm, i.e., an algorithm which is relatively insensitive to rounding errors.
A convolutional neural network does not require to be stable when it is used for economy applications being related with the offline learning. Nevertheless, a convolutional neural network requires to be stable when it...
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A convolutional neural network does not require to be stable when it is used for economy applications being related with the offline learning. Nevertheless, a convolutional neural network requires to be stable when it is used for economy applications being related with the online learning. Therefore, it would be interesting to ensure the stability of a convolutional neural network for economy applications being related with the online learning. In this investigation, a stable algorithm considering a time varying learning rate is proposed to adapt the weights of a stable convolutional neural network. The stable algorithm considering a time varying learning rate is used to improve the learning and to ensure the stability and robustness of the stable convolutional neural network, where the time varying learning rate will obtain big steps when the minimum of the cost function is far, and the time varying learning rate will obtain small steps when the minimum of the cost function is near. The stable convolutional neural network is compared with the principal component analysis neural network, non -negative matrix factorization neural network, and convolutional neural network for economy applications being related with the online learning considering the electrical energy consumption modeling and hybrid chiller modeling.
When solving the linear system ${\bf A}x = {\bf b}$, the condition number $K(A) \equiv \| A \| \| A^{ - 1} \|$ is a useful, albeit often overly conservative, measure of the sensitivity of the solution ${\bf x}$ under...
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When solving the linear system ${\bf A}x = {\bf b}$, the condition number $K(A) \equiv \| A \| \| A^{ - 1} \|$ is a useful, albeit often overly conservative, measure of the sensitivity of the solution ${\bf x}$ under perturbations $\Delta A$ and $\Delta {\bf b}$ to A and ${\bf b}$. We demonstrate how the projection of ${\bf b}$ onto the range space of A, in addition to $K(A)$, can strongly affect the sensitivity of ${\bf x}$ in specific problem instances. Two practical cases are presented in which the sensitivity of ${\bf x}$ can be substantially smaller than that predicted by $K(A)$ alone. In the first example, we characterize a class of Vandermonde matrices and right-hand sides for which accurate algorithms can exist. For the second example, we show that a (fast Fourier transform-) FFT-based fast Poisson solver can produce very accurate results for smooth right-hand sides. Computational examples on the fast Poisson solver are included to illustrate these concepts.
The medial axis transform of a 2D region was introduced by Blum in the 1960's as an aid to the description of biological shape. It is an alternative representation of a region which is often more amenable to analy...
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The medial axis transform of a 2D region was introduced by Blum in the 1960's as an aid to the description of biological shape. It is an alternative representation of a region which is often more amenable to analysis. This property has led to its use in diverse fields including pattern recognition and automatic finite element mesh generation. There are two widely agreed mathematical definitions for the medial axis transform which are closely related. It is shown that these definitions are not in general equivalent, despite being so for many types of region. In this paper, precise mathematical definitions of the medial axis transform and its key points (atoms) are given, and an O(n(2)) algorithm for its computation via those atoms presented. This algorithm is described in terms of simple polygons whose sole boundary consists of circular arcs and straight line segments, then extended to polygons with holes. It is shown how more complex edges could be accommodated. In comparison with existing algorithms it is simple to implement and stable in the presence of geometric degeneracy.
Haptic device enable the user to manipulate the molecules and feel interactions during the docking process in virtual environment on the computer. Implementation of force-torque feedback allows the user to have more r...
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ISBN:
(纸本)9783642223358;9783642223365
Haptic device enable the user to manipulate the molecules and feel interactions during the docking process in virtual environment on the computer. Implementation of force-torque feedback allows the user to have more realistic experience during force simulation and find the optimum docking positions faster. In this paper, we propose a haptic rendering algorithm for biomolecular docking with force-torque feedback. It enables the user to experience six degree-of-freedom (DOF) haptic manipulation in molecular docking process. The linear smoothing method was proposed to improve stability of the haptic rendering during molecular docking. Collaborative docking with two devices was implemented.
In this paper we study a class of Mixed Bivariate Poisson Distributions by extending the Hofmann Distribution from the univariate case to the bivariate case. We show how to evaluate the bivariate aggregate claims dist...
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Within the framework of the one-dimensional model for a tribo-couple consisting of two elastic cylinders accounting for the frictional heat generation on the interface due to the roughness of the contacting dissimilar...
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Within the framework of the one-dimensional model for a tribo-couple consisting of two elastic cylinders accounting for the frictional heat generation on the interface due to the roughness of the contacting dissimilar materials, a problem on the identification of the unknown temperature on one of the limiting surfaces of either inner or outer cylindrical layers is formulated and reduced to an inverse thermoelasticity problem via the use of the circumferential strain given on the other surface. To solve the latter problem, a semi-analytical algorithm is suggested, and its stability with respect to the small errors in the input data is analyzed. The efficiency of the proposed solution algorithm is validated numerically by comparing its results with the solution of a corresponding direct problem. The temperature and thermal stresses in the tribo-couple are analyzed.
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