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Computational and Statistical Aspects of Determining Ship's Position

100%

Drapella A. , Morgaś W.

tom No. 24

5--18

In its mathematical essence, the task of determining ship’s position coordinates, is to minimize appropriately defined goal function. This paper proposes to use the method of conjugate gradient for this purpose. The reason is that calculations may be performed in some seconds time because Microsoft and Apache implemented the conjugate gradient method as a tool called the Solver and embedded this tool in their widely offered and popular spreadsheets, namely Excel and the Open Office Calc, respectively. Further in this paper it is shown how to precisely assess errors of ship’s position coordinates with the Monte Carlo method that employs the Solver.

Matematyczna istota wyznaczania współrzędnych pozycji okrętu to minimalizacja odpowiednio zdefiniowanej funkcji celu. Artykuł proponuje wykorzystanie do tego metody gradientu sprzężonego. Dzięki niej obliczenia mogą być wykonane w kilka sekund, ponieważ Microsoft i Apache zaimplementowały metodę gradientu sprzężonego jako narzędzie nazwane Solver i umieściły je w swych szeroko oferowanych i popularnych arkuszach kalkulacyjnych: Excelu i Open Office Calc. W artykule pokazano także, jak precyzyjnie określić błędy oszacowania współrzędnych pozycji okrętu metodą Monte Carlo.

Efficient Iterative Detection Based on Conjugate Gradient and Successive Over-Relaxation Methods for Uplink Massive MIMO Systems

88%

Labed S. , Aounallah N.

tom nr 2

1--9

Being a crucial aspect of ﬁfth-generation (5G) mobile communications systems, massively multiple-input multipleoutput (mMIMO) architectures are expected to help achieve the highest key performance indicators. However, the huge numbers of antennas used in such systems make it diﬃcult to determine the inversion of the signal channel matrix relied upon by several detection methods, hence posing a problem with accurate estimation of the symbols sent. In this paper, conjugate gradient (CG) and successive over-relaxation (SOR) methods are selected to construct a new iterative approach that avoids the matrix inversion computation issue. This suggested approach for uplink mMIMO detection is based on a joint cascade structure of both iterative methods. The CG method is ﬁrst applied and adjusted for the initial solution, followed by the SOR method in the ﬁnal iterations for terminal computations, resulting in an algorithm with robust performance and low computational complexity. Furthermore, the new hybrid scheme operates based on the relaxation parameter, whose value has a great impact on error performance and, whose optimal determination is necessary. Numerical simulations reveal that the proposed scheme is capable of signiﬁcantly improving signal detection accuracy with minimum complexity. The simulation results indicated that the proposed detector outperforms CG and SOR detectors, achieves close to optimal performance, requires fewer iterations, and reduces complexity.

Empirical analysis of different hybridization strategies for solving systems of nonlinear equations

88%

Singh B. P. , Mäkelä M. M. , Nikulin Y.

tom Vol. 52, No. 3

269--289

This paper considers various hybrid methods for solving a system of nonlinear equations. Extensive numerical experiments confirm the research hypothesis that one particular form of hybridization of the conjugate gradient algorithm with Newton’s method outperforms other hybrid strategies considered in the paper.

Operator-splitting and Lagrange multiplier domain decomposition methods for numerical simulation of two coupled Navier-Stokes fluids

75%

Bresch D. , Koko J.

tom Vol. 16, no 4

419-429

We present a numerical simulation of two coupled Navier-Stokes flows, using operator-splitting and optimization-based nonoverlapping domain decomposition methods. The model problem consists of two Navier-Stokes fluids coupled, through a common interface, by a nonlinear transmission condition. Numerical experiments are carried out with two coupled fluids; one with an initial linear profile and the other in rest. As expected, the transmission condition generates a recirculation within the fluid in rest.