We describe a robust and adaptive implementation of the L-curve criterion. The algorithm locates the corner of a discrete L-curve which is a log–log plot of corresponding residual norms and solution norms of regularized solutions from a method with a discrete regularization parameter (such as truncated SVD or regularizing CG iterations). Our algorithm needs no predefined parameters, and in order to capture the global features of the curve in an adaptive fashion, we use a sequence of pruned L-curves that correspond to considering the curves at different scales. We compare our new algorithm to existing algorithms and demonstrate its robustness by numerical examples
In this paper the minimum ship domain in which a navigator feels comfortable is estimated. That is, we estimate the free space surrounding a ship into which no other ship or object should enter. This is very useful when estimating the maximum flow through a channel or a bridge span. The paper benefits from the introduction of Automatic Identification System (AIS) data as it is now much easier to conduct studies involving a large number of observations. Our observations are based on ships sailing in southern Danish waters during a four year period, and from the observations we estimate how closely ships pass each other and fixed objects in open sea navigation. The main result is the establishment of an empirical minimum ship domain related to a comfortable navigational distance.
The Two-Stage Gasifier was operated for several weeks (465 hours) and of these 190 hours continuously. The gasifier is operated automatically unattended day and night, and only small adjustments of the feeding rate were necessary once or twice a day. The operation was successful, and the output as expected. The engine operated well on the produced gas, and no deposits were observed in the engine afterwards. The bag house filter was an excellent and well operating gas cleaning system. Small amounts of deposits consisting of salts and carbonates were observed in the hot gas heat exchangers. The top of the reactor had to be constructed in some other material.
Abstract.We study the regularization properties of iterative minimum-residual methods applied to discrete ill-posed problems. In these methods, the projection onto the underlying Krylov subspace acts as a regularizer, and the emphasis of this work is on the role played by the basis vectors of these Krylov subspaces. We provide a combination of theory and numerical examples, and our analysis confirms the experience that MIN-RES and MR-II can work as general regularization methods. We also demonstrate theoretically and experimentally that the same is not true, in general, for GMRES and RRGMRES -their success as regularization methods is highly problem dependent. (2000): 65F22, 65F10.
AMS subject classification
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.