Controlled K−g−Fusion Frames in Hilbert C∗−Modules

Controlled frames have been the subject of interest because of its ability to improve the numerical efficiency of iterative algorithms for inverting the frame operator. In this paper, we introduce the concepts of controlled g−fusion frame and controlled K−g−fusion frame in Hilbert C∗−modules and we give some properties. Also, we study the perturbation problem of controlled K−g−fusion frame. Moreover, an illustrative example is presented to support the obtained results.

On Improving Algorithm Efficiency of Gas-Kick Simulations toward Automated Influx Management: A Robertson Differential-Algebraic-Equation Problem Approach

Summary Improved numerical efficiency in simulating wellbore gas-influx behaviors is essential for realizing real-time model-prediction-based gas-influx management in wells equipped with managed-pressure-drilling (MPD) systems. Currently, most solution algorithms for high-fidelitymultiphase-flow models are highly time consuming and are not suitable for real-time decision making and control. In the application of model-predictive controllers (MPCs), long calculation time can lead to large overshoots and low control efficiency. This paper presents a drift-flux-model (DFM)-based gas-influx simulator with a novel numerical scheme for improved computational efficiency. The solution algorithm to a Robertson problem as differential algebraic equations (DAEs) was used as the numerical scheme to solve the control equations of the DFM in this study. The numerical stability and computational efficiency of this numerical scheme and the widely used flux-splitting methods are compared and analyzed. Results show that the Robertson DAE problem approach significantly reduces the total number of arithmetic operations and the computational time compared with the hybrid advection-upstream-splitting method (AUSMV) while maintaining the same prediction accuracy. According to the “Big-O notation” analysis, the Robertson DAE approach shows a lower-order growth of computational complexity, proving its good potential in enhancing numerical efficiency, especially when handling simulations with larger scales. The validation of both the numerical schemes for the solution of the DFM was performed using measured data from a test well drilled with water-based mud (WBM). This study offers a novel numerical solution to the DFM that can significantly reduce the computational time required for gas-kick simulation while maintaining high prediction accuracy. This approach enables the application of high-fidelity two-phase-flow models in model-prediction-based decision making and automated influx management with MPD systems.

Estimation of the numerical efficiency of global optimization methods

Currently, test problems are used to test the effectiveness of new global optimization methods. In this article, we analyze test global optimization problems to test the numerical efficiency of methods for their solution. At present, about 200 test problems of unconditional optimization and more than 1000 problems of conditional optimization have been developed. We can find these test problems on the Internet. However, most of these test problems are not informative for testing the effectiveness of global optimization methods. The solution of test problems of conditional optimization, as a rule, has trivial solutions. This allows the parameters of the algorithms to be tuned before these solutions are obtained. In test problems of conditional optimization, the accuracy of the fulfillment of constraints is important. Often, small errors in the constraints lead to a significant change in the value of an objective function. Construction of a new package of test problems to test the numerical efficiency of global optimization methods and compare the exact quadratic regularization method with existing methods.The author suggests limiting oneself to test problems of unconstrained optimization with unknown solutions. A package of test problems of unconstrained optimization is pro-posed, which includes known test problems with unknown solutions and modifications of some test problems proposed by the author. We also propose to include in this package J. Nie polynomial functions with unknown solutions. This package of test problems will simplify the verification of the numerical effectiveness of methods. The more effective methods will be those that provide the best solutions. The paper compares existing global optimization methods with the exact quadratic regularization method proposed by the author. This method has shown the best results in solving most of the test problems. This paper presents some of the results of the author's numerical experiments. In particular, the best solutions were obtained for test problems with unknown solutions. This method allows solving multimodal problems of large dimensions and only a local search program is required for its implementation.

Controlled g-fusion frame in Hilbert space

Fusion frame is a generalization of frame, which can analyze signals by projecting them onto multidimensional subspaces. Controlled fusion frame as generalization of fusion frame, it can improve the numerical efficiency of iterative algorithms for inverting the fusion frame operators. In this paper, we first introduce the notion of controlled g-fusion frame, discuss several properties of controlled g-fusion Bessel sequence. Then, we present some sufficient conditions and some characterizations of controlled g-fusion frames. Finally, we study the sum of controlled g-fusion frames.

Convergence results of a faster iterative scheme including multi-valued mappings in Banach spaces

In this paper, we study M-iterative scheme in the new context of multi-valued generalized ?-nonexpansive mappings. A uniformly convex Banach space is used as underlying setting for our approach. We also provide a new example of generalized ?-nonexpasive mappings. We connect M iterative scheme and other well known schemes with this example, to show the numerical efficiency of our results. Our results improve and extend many existing results in the current literature.

Approximating Fixed Points of Operators Satisfying (RCSC) Condition in Banach Spaces

Let K be a nonempty subset of a Banach space E. A mapping T:K→K is said to satisfy (RCSC) condition if each a,b∈K, 1/2a−Fa≤a−b⇒Fa−Fb≤1/3a−b+a−Fb+b−Fa. In this paper, we study, under some appropriate conditions, weak and strong convergence for this class of maps through M iterates in uniformly convex Banach space. We also present a new example of mappings with condition (RCSC). We connect M iteration and other well-known processes with this example to show the numerical efficiency of our results. The presented results improve and extend the corresponding results of the literature.