Results 161 to 170 of about 2,092,411 (198)

The Stability of Variable-Stepsize Nordsieck Methods

SIAM Journal on Numerical Analysis, 1983
Conditions are given for the stability of multistep methods that vary the stepsize using the interpolation technique of Nordsieck. If the stepsize selection function is variation-bounded, then these methods are stable. Alternatively there exist constants a, b, c depending on the method and satisfying $a \leqq b < 1 < c$ such that if the stepsize ratio $
Skeel, R. D., Jackson, L. W.
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Parallel tangent methods with variable stepsize

2004 IEEE International Joint Conference on Neural Networks (IEEE Cat. No.04CH37541), 2005
The most widely used algorithm for training multilayer feedforward neural networks is backpropagation. Back-propagation is an iterative gradient descent algorithm. Since its appearance, various methods which modify the conventional BP have been created to improve its efficiency. One such algorithm which uses an adaptive learning rate is backpropagation
Yiannis G. Petalas, Michael N. Vrahatis
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Two high-order multistep methods with offstep points applied with a variable stepsize [PDF]

Journal of Computational and Applied Mathematics, 1990
In this paper we derive new generalized multistep methods with variable stepsize for initial-value problems in ordinary differential equations.
S Filippi
exaly   +2 more sources

Stability of variable and random stepsize LMS

1997 IEEE International Conference on Acoustics, Speech, and Signal Processing, 2002
The stability of variable stepsize LMS (VSLMS) algorithms with uncorrelated stationary Gaussian data is studied. It is found that when the stepsize is determined by the past data, the boundedness of the step size by the usual stability condition of fixed stepsize LMS is sufficient for the stability of VSLMS.
Saul B. Gelfand, Yongbin Wei, James V. Krogmeier   +2 more
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On the Stability of Variable-Stepsize Nordsieck BDF Methods

SIAM Journal on Numerical Analysis, 1987
Die Verf. studieren die asymptotische Stabilität der rückwärts genommenen Differentiationsformeln in Nordsieck-Form auf nichtäquidistanten Gittern. Bei einem Wechsel der Schrittweite wird die Nordsiecksche Interpolationstechnik verwandt. Damit sind bei der Stabilitätsanalyse die Normen der Produkte der sich mit dem Schrittweitenwechsel ebenfalls ...
Calvo, M., Lisbona, F., Montijano, J.
exaly   +2 more sources

The Convergence of Variable-Stepsize, Variable-Formula, Multistep Methods

SIAM Journal on Numerical Analysis, 1984
Die Verff. studieren das Verhalten von Mehrschrittverfahren auf variablen Gittern der Gestalt \[ y_{n+1}=\sum^{s_ n}_{i=0}a_{n,i}y_{n- i}+b_ nh_{n+1}y'\!_{n+1}+\sum^{r_ n}_{i=0}b_{n,i}h_{n- i}y'\!_{n-i} \] mit y'\({}_ i:=f(t_ i,y_ i)\). Die Stabilität des linearen Teils der Verfahren allein hat (unter passenden Voraussetzungen) die des gesamten ...
Crouzeix, M., Lisbona, F. J.
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ESIRK methods and variable stepsize

Applied Numerical Mathematics, 1998
Singly implicit Runge-Kutta methods (SIRK) have been introduced in order to reduce the implementation costs. Many of them, however, have the disadvantage that certain internal stages approximate the solution outside the integration interval. The idea of effective order permits to overcome this difficulty, but leads to a less straightforward ...
Butcher, J. C., Chen, D. J. L.
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Time-transformations for reversible variable stepsize integration

Numerical Algorithms, 1998
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Stephen D. Bond, Benedict J. Leimkuhler
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Variable order and stepsize in general linear methods

Numerical Algorithms, 2019
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Saghir Ahmad, John C. Butcher, Winston L. Sweatman   +2 more
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A Time-Reversible Variable-Stepsize Integrator for Constrained Dynamics

SIAM Journal on Scientific Computing, 1999
The main results of the paper are the design and implementation of variable-stepsize methods for the time-discretization of constrained Euler-Lagrange equations faithful to symplectic and time-reversal symmetry structures of the equations. Symplectic structures are first explored because of the fact that classical equations of motion can be put in ...
Eric Barth, Benedict J. Leimkuhler, Sebastian Reich   +2 more
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