Cloud computing is considered as one of the key drivers for the next generation of mobile networks (e.g., 5G). This is combined with the dramatic expansion in mobile networks, involving millions (or even billions) of ...
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Cloud computing is considered as one of the key drivers for the next generation of mobile networks (e.g., 5G). This is combined with the dramatic expansion in mobile networks, involving millions (or even billions) of subscribers with a greater number of current and future mobile applications (e.g., IoT). Cloud Radio Access Network (C-RAN) architecture has been proposed as a novel concept to gain the benefits of cloud computing as an efficient computing resource, to meet the requirements of future cellular networks. However, the computational complexity of obtaining the channel state information in the full-centralized C-RAN increases as the size of the network is scaled up, as a result of enlargement in channel information matrices. To tackle this problem of complexity and latency, MapReduce framework and fast matrix algorithms are proposed. This paper presents two levels of complexity reduction in the process of estimating the channel information in cellular networks. The results illustrate that complexity can be minimized from O(N-3) to O((N/k)(3)), where N is the total number of RRHs and k is the number of RRHs per group, by dividing the processing of RRHs into parallel groups and harnessing the MapReduce parallel algorithm in order to process them. The second approach reduces the computation complexity from O((N/k)(3)) to O((N/k)(2.807)) using the algorithms of fastmatrix inversion. The reduction in complexity and latency leads to a significant improvement in both the estimation time and in the scalability of C-RAN networks.
Many computational schemes in linear algebra can be studied from the point of view of (discrete) time-varying linear systems theory. For example, the operation 'multiplication of a vector by an upper triangular ma...
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Many computational schemes in linear algebra can be studied from the point of view of (discrete) time-varying linear systems theory. For example, the operation 'multiplication of a vector by an upper triangular matrix' can be represented by a computational scheme (or model) that acts sequentially on the entries of the vector. The number of intermediate quantities ('states') that are needed in the computations is a measure of the complexity of the model. If the matrix is large but its complexity is low, then not only multiplication, but also other operations such as inversion and factorization, can be carried out efficiently using the model rather than the original matrix. In the present paper we discuss a number of techniques in time-varying system theory that can be used to capture a given matrix into such a computational network.
A boundary value problem for Maxwell's equations in the frequency domain with impedance boundary conditions is considered. The problem is reduced to solving a system of two boundary integral equations containing w...
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A boundary value problem for Maxwell's equations in the frequency domain with impedance boundary conditions is considered. The problem is reduced to solving a system of two boundary integral equations containing weakly and strongly singular integrals. For the numerical solution of a system of integral equations, the paper presents a numerical solution method based on piecewise constant approximation and collocation methods. Thus, the original problem is reduced to solving a system of linear algebraic equations with a dense matrix. To effectively solve a system of linear equations, the method of mosaic-skeleton approximations of matrices is used. The specifics of applying the method of mosaic-skeleton approximations in this problem are analyzed.
In this article authors analyse the specifics of parallel implementation of numericalmethods based on integral equations. The necessity to create original parallel subroutines implementing fast matrix algorithms for e...
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In this article authors analyse the specifics of parallel implementation of numericalmethods based on integral equations. The necessity to create original parallel subroutines implementing fast matrix algorithms for efficient work with big dense matrices is stressed out. Specifics of parallel algorithms and calculating capabilities of integral equations method for some aerodynamics and electrodynamics problems are shown.
In this article authors present a new method to construct low-rank approximations of dense huge-size matrices. The method develops mosaic-skeleton method and belongs to kernel-independent methods. In distinction from ...
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In this article authors present a new method to construct low-rank approximations of dense huge-size matrices. The method develops mosaic-skeleton method and belongs to kernel-independent methods. In distinction from a mosaic-skeleton method, the new one utilizes the hierarchical structure of matrix not only to define matrix block structure but also to calculate factors of low-rank matrix representation. The new method was applied to numerical calculation of boundary integral equations that appear from 3D problem of scattering monochromatic electromagnetic wave by ideal-conducting bodies. The solution of model problem is presented as an example of method evaluation.
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