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Linear approximation
About: Linear approximation is a research topic. Over the lifetime, 3901 publications have been published within this topic receiving 74764 citations.
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49 citations
TL;DR: In this paper, an approximation formula for constructing two linear objective functions based on the nonlinear objective function of the equivalent deterministic form (EDF) of the stochastic programming model is presented.
49 citations
TL;DR: The adaptive h-refinement solution of the incompressible MHD equations in stream function form using a stabilized finite element formulation is described, indicating a more accurate resolution of current sheets with higher-order methods than with piecewise-linear approximations.
49 citations
TL;DR: An efficient initial approximation method for multiplicative division and square root is proposed, a modification of the piecewise linear approximation that requires only a bit-wise inversion and a one-bit shift.
Abstract: An efficient initial approximation method for multiplicative division and square root is proposed. It is a modification of the piecewise linear approximation. The multiplication and the addition required for the linear approximation are replaced by only one multiplication with a slight modification of the operand. The same accuracy is achieved. The modification of the operand requires only a bit-wise inversion and a one-bit shift, and can be implemented by a very simple circuit. One clock cycle may be saved, because the addition is removed. The required table size is also reduced, because only one coefficient instead of two has to be stored.
49 citations
TL;DR: A novel convex approximation technique to approximate the original problem by a series of convex subproblems, each of which decomposes across all the cells, which shows that the proposed framework is effective for solving interference management problems in large HetNet.
Abstract: We study the downlink linear precoder design problem in a multicell dense heterogeneous network (HetNet). The problem is formulated as a general sum-utility maximization (SUM) problem, which includes as special cases many practical precoder design problems such as multicell coordinated linear precoding, full and partial per-cell coordinated multipoint transmission, zero-forcing precoding, and joint BS clustering and beamforming/precoding. The SUM problem is difficult due to its nonconvexity and the tight coupling of the users’ precoders. In this paper, we propose a novel convex approximation technique to approximate the original problem by a series of convex subproblems, each of which decomposes across all the cells. The convexity of the subproblems allows for efficient computation, while their decomposability leads to distributed implementation. Our approach hinges upon the identification of certain key convexity properties of the sum-utility objective, which allows us to transform the problem into a form that can be solved using a popular algorithmic framework called block successive upper-bound minimization (BSUM). Simulation experiments show that the proposed framework is effective for solving interference management problems in large HetNet.
49 citations