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A Variable Stepsize, Variable Order Family of Low Complexity
SIAM Journal on Scientific Computing, 2021zbMATH Open Web Interface contents unavailable due to conflicting licenses.
DeCaria, Victor +3 more
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Variable stepsize multivalue collocation methods
Applied Numerical Mathematics, 2023zbMATH Open Web Interface contents unavailable due to conflicting licenses.
A. Moradi, R. D'Ambrosio, B. Paternoster
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Effective Backpropagation Training with Variable Stepsize
Neural Networks, 1997The issue of variable stepsize in the backpropagation training algorithm has been widely investigated and several techniques employing heuristic factors have been suggested to improve training time and reduce convergence to local minima. In this contribution, backpropagation training is based on a modified steepest descent method which allows variable ...
George S., Androulakis +2 more
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The Convergence of Variable-Stepsize, Variable-Formula, Multistep Methods
SIAM Journal on Numerical Analysis, 1984Die 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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On the Stability of Variable-Stepsize Nordsieck BDF Methods
SIAM Journal on Numerical Analysis, 1987Die 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.
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ESIRK methods and variable stepsize
Applied Numerical Mathematics, 1998Singly 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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The Stability of Variable-Stepsize Nordsieck Methods
SIAM Journal on Numerical Analysis, 1983Conditions 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), 2005The 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
Y.G. Petalas, M.N. Vrahatis
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A Time-Reversible Variable-Stepsize Integrator for Constrained Dynamics
SIAM Journal on Scientific Computing, 1999The 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 ...
Barth, Eric +2 more
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Variable stepsize in Cowell's method
BIT, 1989The author proposes a formula which is intended to facilitate fourth order piecewise constant step size implementation of Cowell's method.
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