With acoustic echo cancellation for hands-free communications, dominant nonlinearities occur at the loudspeaker and its amplifier. This contribution addresses memoryless nonlinearities as they are common, e.g., in loudspeaker amplifiers of mobile phone terminals. An NLMS (normalized least mean square)-type adaptation algorithm is investigated which allows simultaneous identification of a nonlin...

In solving stiff systems of ordinary differential equations using BDF methods, Jacobians needed for quasi-Newton iteration are frequently computed using finite differences. Round-off errors in the finite-difference approximation can lead to Newton failures forcing the code to choose its time steps based on “stability” rather than accuracy considerations. When standard stepsize control is used, ...

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 di cult to use them for adaptive stepsize selection and automatic stopping. We propose alternative “big batch” SGD schemes that adaptively grow the batch size ove...

The present paper focuses on the efficient numerical solving of initialvalue problems (IVPs) using digital computers and one-step numerical methods. We start from considering that the integration stepsize is the crucial factor in determining the number of calculations required and the amount of work involved to obtain the approximate values of the exact solution of a certain problem for a given...

This paper concerns the theoretical analysis of step-by-step methods for solving initial value problems in ordinary and partial differential equations. The main theorem of the paper answers a natural question arising in the linear stability analysis of such methods. It guarantees a (strong) version of numerical stability – under a stepsize restriction related to the stability region of the nume...

We present complexity and numerical results for a new asynchronous parallel algorithmic method for the minimization of the sum of a smooth nonconvex function and a convex nonsmooth regularizer, subject to both convex and nonconvex constraints. The proposed method hinges on successive convex approximation techniques and a novel probabilistic model that captures key elements of modern computation...

This paper proposes accelerated subspace optimization methods in the context of image restoration. Subspace optimization methods belong to the class of iterative descent algorithms for unconstrained optimization. At each iteration of such methods, a stepsize vector allowing the best combination of several search directions is computed through a multidimensional search. It is usually obtained by...