Multiple Region Coverage Path Planning for Autonomous Underwater Vehicle.

Coverage path planning methodology for an autonomous underwater vehicle to search multiple non-overlapping regions has been proposed in the paper. The proposed methodology is based on the genetic algorithm (GA). The GA used in the proposed methodology has been tuned for the specific problem, using design of experiment on an equivalent travelling salesman problem benchmark instance. Optimality of the generated paths was analysed through simulation studies. Results indicated that the proposed methodology generated shorter paths in comparison to conventional methods.

Instance-Optimal Goal-Oriented Adaptivity

We consider an adaptive finite element method with arbitrary but fixed polynomial degree {p\geq 1}, where adaptivity is driven by an edge-based residual error estimator. Based on the modified maximum criterion from [L. Diening, C. Kreuzer and R. Stevenson, Instance optimality of the adaptive maximum strategy, Found. Comput. Math. 16 2016, 1, 33–68], we propose a goal-oriented adaptive algorithm and prove that it is instance optimal. More precisely, the goal error is bounded by the product of the total errors (being the sum of energy error plus data oscillations) of the primal and the dual problem, and the proposed algorithm is instance optimal with respect to this upper bound. Numerical experiments underline our theoretical findings.

REMARKS ABOUT ORTHOGONAL MATCHING PURSUIT ALGORITHMS

The orthogonal matching pursuit (OMP) is a popular decoder to recover sparse signal in compressed sensing. Our aim is to investigate the theoretical properties of OMP. In particular, we show that the OMP decoder can give (p, q) instance optimality for a large class of encoders with 1 ≤ p ≤ q ≤ 2 and (p, q) ≠ (2, 2).

A Note on Stability and Instance Optimality in Compressed Sensing

In this note, it is proved that every -sparse signal vector can be recovered stably from the measurement vector via minimization as soon as the restricted isometry constant of the measurement matrix is smaller than . Note that our results contain the case of noisy data, therefore previous known results in the literature are extent and improved. Also we obtain the results on the stability and instance optimality for some random measurement matrices.