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The methods of dynamical reconstruction of an input in a system of ordinary differential equations

JOURNAL OF INVERSE AND ILL-POSED PROBLEMS 2021年第1期29卷 125-156页

作者： Maksimov, Vyacheslav, I Krasovskii Inst Math & Mech UB RAS Dept Differential Equat S Kovalevskaya Str 16 Ekaterinburg 620108 Russia

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.

关键词： Dynamical inverse problem feedback stable algorithm

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POSITIVE, MONOTONE, AND S-CONVEX C(1)-HISTOPOLATION ON RECTANGULAR GRIDS

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COMPUTING 1993年第1期50卷 19-30页

作者： SCHMIDT, JW 1. Institut für Numerische Mathematik Technische Universit?t Dresden Mommsenstrasse 13 D-O-8027 Dresden Federal Republic of Germany

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.

关键词： SHAPE PRESERVING C(1)-HISTOPOLATION SUFFICIENT CONDITIONS stable algorithm

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AUTOMATIC A PRIORI ROUND-OFF ANALYSIS .1. ARITHMETIC CONDITIONS

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COMPUTING 1972年第1-2期10卷 97-106页

作者： MILLER, W PENN STATE UNIV COMP SCI DEPTUNIVERSITY PARKPA 16802

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.

关键词： Computational Mathematic Precise Definition stable algorithm Algebraic Process

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stable convolutional neural network for economy applications

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ENGINEERING APPLICATIONS OF ARTIFICIAL INTELLIGENCE 2024年 132卷

作者： Rubio, Jose de Jesus Garcia, Donaldo Rosas, Francisco Javier Hernandez, Mario Alberto Pacheco, Jaime Zacarias, Alejandro Inst Politecn Nacl Esime Azcapotzalco Secc Estudios Posgrad Invest Ave Granjas 682Col St Catarina Mexico City 02250 Mexico Inst Politecn Nacl Ctr Invest Comp Ave Juan Dios BatizCol San Pedro Zacatenco Mexico City 07738 Mexico

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.

关键词： Convolutional neural network stable algorithm Learning rate Economy applications Electrical energy consumption Hybrid chiller

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EFFECTIVELY WELL-CONDITIONED LINEAR-SYSTEMS

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SIAM JOURNAL ON SCIENTIFIC AND STATISTICAL COMPUTING 1988年第6期9卷 963-969页

作者： CHAN, TF FOULSER, DE YALE UNIV DEPT COMP SCINEW HAVENCT 06520

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.

关键词： 65F35 65F05 65G05 condition number stable algorithm Bj?rk–Pereyra algorithm fast Poisson solver physical stability error analysis

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stable computation of the 2D medial axis transform

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INTERNATIONAL JOURNAL OF COMPUTATIONAL GEOMETRY & APPLICATIONS 1998年第5-6期8卷 577-598页

作者： Evans, G Middleditch, A Miles, N Oxford Mol Ltd Oxford OX4 4GA England Brunel Univ Ctr Geometr Modelling & Design Uxbridge UB8 3PH Middx England Pathtrace Engn Syst Ltd Reading RG2 0NH Berks England

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.

关键词： medial axis transform 2D MAT stable algorithm

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Six Degree-of-Freedom Haptic Rendering for Biomolecular Docking

Six Degree-of-Freedom Haptic Rendering for Biomolecular Dock...

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International Conference on Cyberworlds (CW)

作者： Hou, Xiyuan Sourina, Olga Nanyang Technol Univ Singapore Singapore

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.

关键词： haptic rendering biomolecular docking torque feedback stable algorithm collaboration

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On the Distribution of the Surplus Prior to Ruin in a Discrete Semi-Markov Risk Model

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ASTIN Bulletin 2001年第2期31.0卷 255-273页

作者： Reinhard, J.M. Snoussi, M. Université Libre de Bruxelles Belgium Secura Belgian Re Belgium Université Libre de Bruxelles B-1050 Bruxelles Campus de la plaine CP 210 Belgium

In this paper we extend the work of Reinhard and Snoussi (2000) by developing a recursive system for finding the distribution of the surplus prior to ruin in a discrete semi-Markov risk model. © 2001, Internation... 详细信息

关键词： Probability of ruin recursive calculation stable algorithm surplus prior to ruin

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The Mixed Bivariate Hofmann Distribution

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ASTIN Bulletin 2001年第1期31卷 123-138页

作者： Walhin, J.F. Paris, J. Université Catholique de Louvain Belgium SECURA Belgian Re 1000 Bruxelles Rue Montoyer 12 Belgium

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 distribution and we fit some insurance portfolios given in the literature. This study typically extends the use of the Bivariate Independent Poisson Distribution, the Mixed Bivariate Negative Binomial and the Mixed Bivariate Poisson Inverse Gaussian Distribution. © 2001, International Actuarial Association. All rights reserved.

关键词： aggregate claims distribution Hofmann Distribution maximum likelihood Mixed Bivariate Independent Poisson Distributions recursive algorithm stable algorithm

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Inverse Thermoelastic Analysis of a Cylindrical Tribo-Couple

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MATERIALS 2021年第10期14卷 2657-2657页

作者： Kushnir, Roman Yasinskyy, Anatoliy Tokovyy, Yuriy Hart, Eteri Natl Acad Sci Ukraine Pidstryhach Inst Appl Problems Mech & Math UA-79060 Lvov Ukraine Natl Univ Lviv Polytech Inst Appl Math & Fundamental Sci Dept Appl Math UA-79013 Lvov Ukraine Oles Honchar Dnipro Natl Univ Dept Theoret & Comp Mech UA-49010 Dnipro Ukraine

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.

关键词： tribo-couple cylindrical layers frictional heating unknown thermal loading inverse thermoelasticity problem Volterra integral equation stable algorithm

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