Related papers: Extension and convergence analysis of Iterative Fi…
In this paper, we derive a practical, general framework for creating adaptive iterative (linearization or splitting) algorithms to solve multi-physics problems. This means that, given an iterative method, we derive \textit{a posteriori}…
Within the study of uncertain dynamical systems, iterated random functions are a key tool. There, one samples a family of functions according to a stationary distribution. Here, we introduce an extension, where one sample functions…
Ensemble filters implement sequential Bayesian estimation by representing the probability distribution by an ensemble mean and covariance. Unbiased square root ensemble filters use deterministic algorithms to produce an analysis (posterior)…
The analysis of the time-frequency content of a signal is a classical problem in signal processing, with a broad number of applications in real life. Many different approaches have been developed over the decades, which provide alternative…
We introduce a new iterative method to recover a real compact supported potential of the Schr\"odinger operator from their fixed angle scattering data. The method combines a fixed point argument with a suitable approximation of the…
A matrix approach to continuous iteration is proposed for general formal series. It leads, in particular, to an order{to{order iteration of the exponential function, and consequently to an algorithmic approach to tetration. Lower{order…
The Topological Signal Processing (TSP) framework has been recently developed to analyze signals defined over simplicial complexes, i.e. topological spaces represented by finite sets of elements that are closed under inclusion of subsets…
A family of fixed-point iterations is proposed for the numerical computation of traveling waves and localized ground states. The methods are extended versions of Petviashvili type, and they are applicable when the nonlinear term of the…
The empirical wavelet transform is an adaptive multiresolution analysis tool based on the idea of building filters on a data-driven partition of the Fourier domain. However, existing 2D extensions are constrained by the shape of the…
Non-linear filtering approaches allow to obtain decompositions of images with respect to a non-classical notion of scale, induced by the choice of a convex, absolutely one-homogeneous regularizer. The associated inverse scale space flow can…
We report the first application of complex symmetric wavelets to the numerical simulation of a nonlinear signal propagation model. This model is the so-called nonlinear Schrodinger equation that describes, for instance, the evolution of the…
In this paper, we compare two optimization algorithms using full Hessian and approximation Hessian to obtain numerical spherical designs through their variational characterization. Based on the obtained spherical design point sets, we…
In this paper we generalize and improve a recently developed domain decomposition preconditioner for the iterative solution of discretized Helmholtz equations. We introduce an improved method for transmission at the internal boundaries…
Deep learning based on deep neural networks of various structures and architectures has been powerful in many practical applications, but it lacks enough theoretical verifications. In this paper, we consider a family of deep convolutional…
Data assimilation is the task to combine evolution models and observational data in order to produce reliable predictions. In this paper, we focus on ensemble-based recursive data assimilation problems. Our main contribution is a hybrid…
An iterative coupling algorithm based on restricted additive Schwarz domain decomposition is investigated to co-simulate electrical circuits with hybrid electromagnetic (EMT) and transient stability (TS) modeled using dynamic phasors. This…
Data augmentation in feature space is effective to increase data diversity. Previous methods assume that different classes have the same covariance in their feature distributions. Thus, feature transform between different classes is…
Trend filtering is a modern approach to nonparametric regression that is more adaptive to local smoothness than splines or similar basis procedures. Existing analyses of trend filtering focus on estimating a function corrupted by…
Nonsinusoidal oscillatory signals are everywhere. In practice, the nonsinusoidal oscillatory pattern, modeled as a 1-periodic wave-shape function (WSF), might vary from cycle to cycle. When there are finite different WSFs, $s_1,\ldots,s_K$,…
The closed feedback loop in recommender systems is a common setting that can lead to different types of biases. Several studies have dealt with these biases by designing methods to mitigate their effect on the recommendations. However, most…