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This paper illustrates the development of a recursive QR technique for the analysis of transient events, such as disruptions or scenario evolution, in fusion devices with three-dimensional conducting structures using an integral eddy current formulation. An integral formulation involves the solution, at each time step, of a large full linear system. For this reason, a direct solution is impractical in terms of time and memory consumption. Moreover, typical fusion devices show a symmetric/periodic structure. This can be properly exploited when the plasma and other sources possess the same symmetry/periodicity of the structure. Indeed, in this case, the computation can be reduced to only a single sector of the overall structure. In this work the periodicity and the symmetries are merged in the recursive QR technique, exhibiting a huge decrease in the computational cost. Finally, the proposed technique is applied to a realistic large-scale problem related to the International Thermonuclear Experimental Reactor (ITER).

In the transmission line inspection operation, the flying robotic arm with good maneuverability can replace the manpower to complete a variety of scenes that are in danger or difficult to reach by manpower for grasping operations. In this paper, based on the D-H matrix, the tandem robotic arm is initially modeled, combined with the Lagrange equation and the characteristics of the robotic arm, to construct the robotic arm dynamics model. Construct the visual servo frame of the flying robotic arm and define the coordinate system of the visual servo system. Get the center point of the grasping frame by grasping the target, establish the camera coordinate system, and realize the position-based visual servo control. Drawing on the predatory action of the bald eagle in biology, set the grasping strategy of the flying robotic arm. Verify the application effect of visual servo in UAV robotic arm grasping through simulation experiments. The random motion speed of the UAV in three-dimensional space is analyzed, and the maximum speeds of roll, pitch and yaw of the target in the motion process are about 1.311 rad/s, 0.825 rad/s, and 1.239 rad/s. In the estimation accuracy of the flying robotic arm's position, the overlap between the true value of the UAV's position and the trajectory of the estimation value is high, and the x-axis only appears smaller errors in 15s, 26s, and 32s, respectively, at 15s, 26s and 32s. There is a small error of 0.013, 0.003, 0.002m, respectively, and the model has a high accuracy in estimating the position of the UAV.

Recently, Dehghan et al. presented the diagonal and off-diagonal splitting (DOS) iteration method for solving the linear systems 𝒜x = b [3]. In this paper, we improve its convergence rate with extrapolation. Also convergence analysis of extrapolated DOS (EDOS) iterative method is studied by giving an upper bound of the extrapolation parameter, then consistency of EDOS and its optimal extrapolation parameter are discussed. Finally, several numerical examples are given to show the efficiency of the presented method.

The aim of this paper is to obtain new lower bounds for the smallest singular value for some special subclasses of nonsingular H-matrices. This is done in two steps: first, unifying principle for deriving new upper bounds for the norm 1 of the inverse of an arbitrary nonsingular H-matrix is presented, and then, it is combined with some well-known upper bounds for the infinity norm of the inverse. The importance and efficiency of the results are illustrated by an example from ecological modelling, as well as on a type of large-scale matrices posessing a block structure, arising in boundary value problems.

In this paper, we propose a preconditioned general modulus-based matrix splitting iteration method for solving modulus equations arising from linear complementarity problems. Its convergence theory is proved when the system matrix is an H + -matrix, from which some new convergence conditions can be derived for the (general) modulus-based matrix splitting iteration methods. Numerical results further show that the proposed methods are superior to the existing methods.

In this paper, based on global relaxed parallel multisplitting USAOR (GUSAOR) method presented by Zhang et al. (Appl Math Comput 20:121–132, 2008) and similar ideas used by Zhang and Li (Comput Math Appl 67:1954–195, 2014), we further analyze global relaxed parallel multisplitting USAOR (GUSAOR) method and obtain the weaker convergence results compared to Zhang et al.’s when the system matrix is an H-matrix. Moreover, convergence graph and numerical examples clearly show that our new convergence domain is wider.

The article described two full multidimensional controllers applied to steer a real vessel named ‘Blue Lady’ that is used by the Foundation for Safety of Navigation and Environment Protection at its training and research facility loacted at Silm lake in Poland. Both controllers were based on different approaches, but finally gave similar results. The first part describes the object to be controlled which is a training ship used for training of navigators in various conditions, areas and manoeuvres. This is followed by a short description of the theory for both controllers, Robust and Linear Matrix Inequalities (LMI). Next real time trials are described, which are 3 different manouvers for low velocities, executed by both LMI and Robust contrllers. In these trials ‘Blue Lady’ velocities, silhouete trajectory ans wind data are recorded. Finally the quality of work for both controllers is collected in two tables.

Memories play a very important role in computing systems due to the continuous advancements in technology. They are used to store data that is used for proper system operations. Memory architectures that are more intricately designed are more prone to radiation-induced errors such as single bit upsets (SBU) and multiple bit upsets (MBU). Error correction codes (ECC) are used to recover the corrupted data that are stored in memories. H-matrix-based ECC is the commonly used ECC for memories. On the other side, the correction masking (CM) technique was added to ECC to mask the correctable error patterns. CM technique protects the error-free bits while correcting erroneous bits. In this paper, optimized H-matrices are presented. These matrices are used to design an ECC with the CM technique to correct 2-bit to 7-bit adjacent errors. The result shows there is a reduction in the power of 2, 3, and 4 adjacent bit errors by 19.009%, 4.615%, and 27.934% respectively.

The concept of the generalized Perron complement concerning a nonnegative irreducible matrix was proposed by L. Z. Lu in 2002, and it was used to construct an algorithm for estimating the boundary of the spectral radius. In this study, we consider the properties of generalized Perron complements of nonnegative irreducible and diagonally dominant matrices. Moreover, we analyze the closure property of the generalized Perron complements of nonnegative irreducible$ H $ -matrices under certain conditions.

In this paper, we obtain a new estimate for the (product) γ -diagonally dominant degree of the Schur complement of matrices. As applications we discuss the localization of eigenvalues of the Schur complement and present several upper and lower bounds for the determinant of strictly γ -diagonally dominant matrices, which generalizes the corresponding results of Liu and Zhang (SIAM J. Matrix Anal. Appl. 27 (2005) 665-674).