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  • Articles  (153)
  • Neural networks  (85)
  • stability  (68)
  • Springer  (153)
  • American Association for the Advancement of Science
  • Wiley
  • Computer Science  (153)
  • 1
    Electronic Resource
    Electronic Resource
    On the stability of multistep formulas for Volterra integral equations of the second kind (1980)
    Springer
    Computing 24 (1980), S. 341-347 
    Details
    ISSN: 1436-5057
    Keywords: Numerical analysis ; Volterra integral equations of the second kind ; stability
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science
    Description / Table of Contents: Zusammenfassung Ziel dieser Arbeit ist es, die Stabilitätseigenschaften einer Klasse Volterrascher Integralgleichungen zweiter Art zu untersuchen. Unsere Behandlung ist der üblichen Stabilitätsanalyse ähnlich, in der die Kernfunktionen zu einer im voraus beschränkten Klasse von Testfunktionen gehören. Wir haben die Klasse der “endlich zerlegbaren” Kerne betrachtet. Stabilitätsbedingungen werden abgeleitet und verglichen mit den Bedingungen für die einfache Testgleichung. Es zeigt sich, daß die neuen Kriteria einschränkender sind als die konventionellen Bedingungen. Der praktische Wert wird getestet durch numerische Experimente mit der Trapezregel.
    Notes: Abstract The purpose of this paper is to analyse the stability properties of a class of multistep methods for second kind Volterra integral equations. Our approach follows the usual analysis in which the kernel function is a priori restricted to a special class of test functions. We consider the class of finitely decomposable kernels. Stability conditions will be derived and compared with those obtained with the simple test equation. It turns out that the new criteria are more severe than the conventional conditions. The practical value is tested by numerical experiments with the trapezoidal rule.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02237819
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  • 2
    Electronic Resource
    Electronic Resource
    Box schemes on quadrilateral meshes (1993)
    Springer
    Computing 51 (1993), S. 271-292 
    Details
    ISSN: 1436-5057
    Keywords: 65N15 ; 65N99 ; 35A40 ; Box method ; boundary value problem ; finite volume method ; variational formulation ; stability ; error bounds
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science
    Description / Table of Contents: Zusammenfassung Box-Methoden (Finite-Volumen-Methoden) sind verbreitete Verfahren zur Lösung physikalischer Erhaltungsgleichungen, insbesondere in der Strömungsmechanik. In dieser Arbeit werden zwei Methoden für elliptische Differentialgleichungen untersucht, die Diagonal-Boxen und die Schwerpunkt-Boxen. Da die Box-Methoden im Sinne von Petrov-Galerkin-Verfahren interpretiert werden können, erhält man vergleichbar zur Finiten-Element-Methode eine variationsrechnerische Stabilitäts- und Fehleranalyse. Damit werdenO(h)- undO(h 2)-Fehlerabschätzungen hergeleitet. Lokale Eigenwertprobleme führen zu Stabilitätsaussagen. Allerdings ergibt sich eine Abhängigkeit von der Anzahl und Art gestörter Vierecke. Insbesondere die Diagonal-Boxen sind anfällig für lokale Störungen.
    Notes: Abstract Box schemes (finite volume methods) are widely used in fluiddynamics, especially for the solution of conservation laws. In this paper two box-schemes for elliptic equations are analysed with respect to quadrilateral meshes. Using a variational formulation, we gain stability theorems for two different box methods, namely the so-called diagonal boxes and the centre boxes. The analysis is based on an elementwise eigenvalue problem. Stability can only be guaranteed under additional assumptions on the geometry of the quadrilaterals. For the diagonal boxes unsuitable elements can lead to global instabilities. The centre boxes are more robust and differ not so much from the finite element approach. In the stable case, convergence results up to second order are proved with well-known techniques.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02238536
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  • 3
    Electronic Resource
    Electronic Resource
    A note on stability investigations for Rosenbrock-type methods for quasilinear-implicit differential equations (1996)
    Springer
    Computing 56 (1996), S. 47-59 
    Details
    ISSN: 1436-5057
    Keywords: 65 L 05 ; Rosenbrock-type methods ; quasilinear-implicit differential equations ; stability
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science
    Description / Table of Contents: Zusammenfassung Bei der Lösung quasilinear-impliziter ODEs mittels Rosenbrock-Typ-Methoden können trotz guter Stabilitätseigenschaften (A- bzw. L-Stabilität) des Grundverfahrens Stabilitätsprobleme auftreten. Diese Schwierigkeiten sind auf Ungenauigkeiten bei der Berechnung künstlich eingeführter Komponenten (Überführung in DAEs) zurückzuführen. Die Arbeit untersucht die Ursachen für diese Effekte und zeigt Möglichkeiten, diese zu überwinden.
    Notes: Abstract The solution of quasilinear-implicit ODEs using Rosenbrock type methods may suffer from stability problems despite stability properties such as A-stability or L-stability, respectively. These problems are caused by inexact computation of artificial introduced components (transformation to DAE system). The paper investigates the source of the numerical difficulties and shows modifications to overcome them.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02238291
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  • 4
    Electronic Resource
    Electronic Resource
    A bifurcation analysis of the nonlinear parametric programming problem (1990)
    Springer
    Mathematical programming 47 (1990), S. 117-141 
    Details
    ISSN: 1436-4646
    Keywords: Bifurcation ; singularity ; parametric programming ; stability
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract The structure of solutions to the nonlinear parametric programming problem with a one dimensional parameter is analyzed in terms of the bifurcation behavior of the curves of critical points and the persistence of minima along these curves. Changes in the structure of the solution occur at singularities of a nonlinear system of equations motivated by the Fritz John first-order necessary conditions. It has been shown that these singularities may be completely partitioned into seven distinct classes based upon the violation of one or more of the following: a complementarity condition, a constraint qualification, and the nonsingularity of the Hessian of the Lagrangian on a tangent space. To apply classical bifurcation techniques to these singularities, a further subdivision of each case is necessary. The structure of curves of critical points near singularities of lowest (zero) codimension within each case is analyzed, as well as the persistence of minima along curves emanating from these singularities. Bifurcation behavior is also investigated or discussed for many of the subcases giving rise to a codimension one singularity.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01580856
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  • 5
    Electronic Resource
    Electronic Resource
    Characterization of stable matchings as extreme points of a polytope (1992)
    Springer
    Mathematical programming 54 (1992), S. 57-67 
    Details
    ISSN: 1436-4646
    Keywords: Matchings ; stability ; extreme points ; polytope
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract The purpose of this paper is to extend a modified version of a recent result of Vande Vate (1989) which characterizes stable matchings as the extreme points of a certain polytope. Our proofs are simpler and more transparent than those of Vande Vate.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01586041
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  • 6
    Electronic Resource
    Electronic Resource
    Quantitative stability of variational systems: III.ε-approximate solutions (1993)
    Springer
    Mathematical programming 61 (1993), S. 197-214 
    Details
    ISSN: 1436-4646
    Keywords: Epi-convergence ; epi-distance ; stability ; convex optimization ; approximate solutions ; subgradients ; level sets
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract We prove that theε-optimal solutions of convex optimization problems are Lipschitz continuous with respect to data perturbations when these are measured in terms of the epi-distance. A similar property is obtained for the distance between the level sets of extended real valued functions. We also show that these properties imply that theε-subgradient mapping is Lipschitz continuous.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01582147
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  • 7
    Electronic Resource
    Electronic Resource
    The spectral accuracy of a fully-discrete scheme for a nonlinear third order equation (1990)
    Springer
    Computing 44 (1990), S. 187-196 
    Details
    ISSN: 1436-5057
    Keywords: 65M10 ; Spectral method ; stability ; stability threshold
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science
    Description / Table of Contents: Zusammenfassung Zur numerischen Lösung einer nichtlinearen Differentialgleichung dritter Ordnung, herrührend aus einem Strömungsproblem bei Gasteilchen, wird ein zeitdiskreter Pseudo-spektral-Algorithmus vorgeschlagen. Stabilität und Konvergenz des neuen Differenzenverfahrens werden analysiert. Numerische Vergleiche mit bestehenden Differenzenschemata sprechen klar zugunsten des neuen Verfahrens.
    Notes: Abstract A time-discrete pseudospectral algorithm is suggested for the numerical solution of a nonlinear third order equation arising in fluidization. The nonlinear stability and convergence of the new scheme are analyzed. Numerical comparisons with available finite-difference methods are also reported which clearly indicate the superiority of the new scheme.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02262215
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  • 8
    Electronic Resource
    Electronic Resource
    Second-order explicit characteristic difference schemes for quasilinear hyperbolic systems (1985)
    Springer
    Computing 35 (1985), S. 85-91 
    Details
    ISSN: 1436-5057
    Keywords: 65M05 ; 65M10 ; 65M25 ; Second order ; characteristic difference schemes ; quasilinear hyperbolic systems ; stability
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science
    Description / Table of Contents: Zusammenfassung Wir stellen ein Charakteristikenverfahren zweiter Ordnung für die numerische Lösung der Anfangswertaufgabe von quasilinearen hyperbolischen Systemen vor und beweisen die Stabilität des Verfahrens für Systeme mit konstanten Koeffizienten.
    Notes: Abstract We present two-step, second-order explicit characteristic difference schemes for the numerical solution of initialvalue problems for quasilinear hyperbolic system and show that the method is stable for systems with constant coefficients.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02240149
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  • 9
    Electronic Resource
    Electronic Resource
    Nichtlineare Stabilität und Phasenuntersuchung adaptiver Nyström-Runge-Kutta-Methoden (1985)
    Springer
    Computing 35 (1985), S. 325-344 
    Details
    ISSN: 1436-5057
    Keywords: 65L05 ; Numerical analysis ; Nyström methods ; stiff problems ; stability
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science
    Description / Table of Contents: Abstract The stability of adaptive Nyström-Runge-Kutta procedures is studied for a wide class of nonlinear stiff systems of second order differential equations. We show that for a large class of semi-discrete hyperbolic and parabolic problems the restriction of the stepsize is not due to the stiffness of the differential equation. Furthermore we use the scalar test equation $$y'' = - \omega ^2 y + q \cdot e^{iv(t - t_0 )} $$ to derive conditions which ensure that the numerical forced oscillation is in phase with the analytical forced oscillation. The order of adaptive Nyström-Runge-Kutta methods (with a stability-matrix based on a diagonal Padéapproximation) for which the forced oscillation is in phase with its analytical counterpart cannot be greater than two. This barrier of order is not true forr-stage implicit Nyström methods of orderp=2r.
    Notes: Zusammenfassung Für eine umfangreiche Klasse nichtlinearer steifer Differentialgleichungssysteme zweiter Ordnung wird die Stabilität adaptiver Nyström-Runge-Kutta-Verfahren untersucht. Wir zeigen, daß für eine große Klasse semidiskretisierter hyperbolischer und parabolischer Probleme die Restriktion der Schrittweite unabhängig von der Steifheit des Differentialgleichungssystems ist. Weiterhin verwenden wir die skalare Testgleichung $$y'' = - \omega ^2 y + q \cdot e^{iv(t - t_0 )} $$ und geben Bedingungen dafür an, daß die numerische erzwungene Schwingung mit der analytischen erzwungenen Schwingung in Phase ist. Die Konsistenzordnung adaptiver Nyström-Runge-Kutta-Verfahren (mit einer Stabilitätsmatrix, die auf einer diagnolen Padé-Approximation beruht), für die die erzwungene Schwingung mit ihrem analytischen Gegenstück in Phase ist, kann nicht größer als zwei sein. Diese Ordnungsbarriere gilt nicht fürr-stufige implizite Nyström-Methoden der Ordnungp=2r.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02240198
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  • 10
    Electronic Resource
    Electronic Resource
    Stationary waiting time derivatives (1992)
    Springer
    Queueing systems 12 (1992), S. 369-389 
    Details
    ISSN: 1572-9443
    Keywords: Perturbation analysis ; stability ; stochastic difference equations ; simulation
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science
    Notes: Abstract We investigate the stability of waiting-time derivatives when inputs to a queueing system-service times and interarrival times-depend on a parameter. We give conditions under which the sequence of waiting-time derivatives admits a stationary distribution, and under which the derivatives converge to the stationary regime from all initial conditions. Further hypotheses ensure that the expectation of a stationary waiting-time derivative is, in fact, the derivative of the expected stationary waiting time. This validates the use of simulation-based infinitesimal perturbation analysis estimates with a variety of queueing processes. We examine waiting-time sequences satisfying recursive equations. Our basic assumption is that the input and its derivatives are stationary and ergodic. Under monotonicity conditions, the method of Loynes establishes the convergence of the derivatives. Even without such conditions, the derivatives obey a linear difference equation with random coefficients, and we exploit this fact to find stability conditions.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01158809
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