We consider variable stepsize time approximations of holomorphic semigroups on general Banach spaces. For strongly A(0)-acceptable rational functions a general stability theorem is proved, which does not impose any constraint on the ratios between stepsizes.

A new optical trapping study shows that the stepsize of cytoplasmic dynein varies according to the applied force, suggesting that this motor can change gear. Complementary biochemical kinetic work on yeast dynein mutants hints at the allosteric mechanisms involved.

This article addresses the problem of the non-unitary joint block diagonalization of a given set of complex matrices. Two new algorithms are provided: the first is based on a classical gradient approach and the second is based on a relative gradient approach. For each algorithm, two versions are provided: the fixed stepsize and the optimal stepsize version. Computer simulations are provided to ...

This paper describes a regularized variant of the alternating direction method of multipliers (ADMM) for solving linearly constrained convex programs. It is shown that the pointwise iteration-complexity of the new method is better than the corresponding one for the standard ADMM method and that, up to a logarithmic term, is identical to the ergodic iteration-complexity of the latter method. Our...

Splitting methods are frequently used in solving stiff differential equations, it is common to split the system of equations into a stiff and a nonstiff part. The classical theory for the local order of consistency is valid only for stepsizes which are smaller than what one would typically prefer to use in the integration. Error control and stepsize selection devices based on classical local or...

In this paper, a new adaptive step-size discrete power control scheme is proposed, based on the review of practical power control schemes implemented in the IS-95, CDMA2000 and WCDMA wireless systems, and the power control algorithms proposed in literature. The transmit power is controlled in discrete power domain while using the idea of the most popular power control algorithm (e.g. DCPC) in p...

This article proposes a new algorithm for solving a class of composite convex-concave saddlepoint problems. The new algorithm is a special instance of the hybrid proximal extragradient framework in which a Nesterov’s accelerated variant is used to approximately solve the prox subproblems. One of the advantages of the new method is that it works for any constant choice of proximal stepsize. More...

Classical stochastic gradient methods for optimization rely on noisy gradient approximations that become progressively less accurate as iterates approach a solution. The large noise and small signal in the resulting gradients makes it difficult to use them for adaptive stepsize selection and automatic stopping. We propose alternative “big batch” SGD schemes that adaptively grow the batch size o...

This paper presents a unified framework for the analysis of several discrete time adaptive parameter estimation algorithms, including RML with nonvanishing stepsize, several ARMAX identifiers, the Landau-style output error algorithms, and certain others for which no stability proof has yet appeared. A general algorithmic form is defined, incorporating a linear time-varying regressor '. filter a...

This letter analyses the convergence behaviour of the transform domain least mean square (TDLMS) adaptive filtering algorithm which is based on a well known interpretation of the variable stepsize algorithm. With this interpretation, the analysis is considerably simplified. The time varying stepsize is implemented by the modified power estimator to redistribute the spread power after transforma...