Abstract Dynamical low-rank integrators for matrix differential equations recently attracted a lot of attention and have proven to be very efficient in various applications. In this paper, we propose novel strategy choosing the rank projector-splitting integrator Lubich Oseledets adaptively. It is based on combination error estimators local time-discretization with aim balance both. This ensure...

In variational data assimilation (VDA) for meteorological and/or oceanic models, the assimilated fields are deduced by combining the model and the gradient of a cost functional measuring discrepancy between model solution and observation, via a first-order optimality system. However, existence and uniqueness of the VDA problem along with convergence of the algorithms for its implementation depe...

Starting from discrete event simulations based on sampled data we simulate the interplay between product density and flux. Data-fitting helps to determine the right parameters for clearing functions to close first and second order conservation laws. For the first order case well-known relations from M/M/1-queuing theory can be reproduced and numerically extended to transient behavior. To includ...

in this paper, an optimal control of quadratic performance index with nonlinear constrained is presented. the sine-cosine wavelet operational matrix of integration and product matrix are introduced and applied to reduce nonlinear differential equations to the nonlinear algebraic equations. then, the newton-raphson method is used for solving these sets of algebraic equations. to present ability ...

In this paper, we develop a novel approach to the problem of learning sparse representations in the context of fused sparsity and unknown noise level. We propose an algorithm, termed Scaled Fused Dantzig Selector (SFDS), that accomplishes the aforementioned learning task by means of a second-order cone program. A special emphasize is put on the particular instance of fused sparsity correspondin...