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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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61 citations
TL;DR: Two closed-form relations are shown that express the frequency and amplitude of the generated oscillation as functions of the parameters of the model Matsuoka neural oscillator.
Abstract: Although the Matsuoka neural oscillator, which was originally proposed as a model of central pattern generators, has widely been used for various robots performing rhythmic movements, its characteristics are not clearly explained even now. This article shows two closed-form relations that express the frequency and amplitude of the generated oscillation as functions of the parameters of the model. Although they are derived based on a rough linear approximation, they accord with the result obtained by a simulation considerably. The obtained relations also give us some nontrivial predictions about the properties of the oscillator.
60 citations
TL;DR: An algorithm for the problem of orthogonal ℓ1 fitting of discrete data is presented, along with numerical results of its application to some data sets.
Abstract: The problem is considered of orthogonal l1 fitting of discrete data. Local best approximations are characterized and the question of the robustness of these solutions is considered. An algorithm for the problem is presented, along with numerical results of its application to some data sets.
60 citations
TL;DR: In this article, the authors derived a second-order Taylor series approximation of the differential range for the polar format algorithm for spotlight synthetic aperture radar (SAR) and provided a simple and concise derivation of both the far-field linear approximation, which forms the basis of the PFA, and the corresponding approximation limits based on the secondorder terms of the approximation.
Abstract: The polar format algorithm (PFA) for spotlight synthetic aperture radar (SAR) is based on a linear approximation for the differential range to a scatterer. We derive a second-order Taylor series approximation of the differential range. We provide a simple and concise derivation of both the far-field linear approximation of the differential range, which forms the basis of the PFA, and the corresponding approximation limits based on the second-order terms of the approximation.
60 citations
TL;DR: The stochastic gradient algorithm using a simplified arithmetic using a power-of-two quantizer is used for the input of the multiplier to reduce the multiplication to at most a simple shift.
Abstract: The stochastic gradient algorithm using a simplified arithmetic is analyzed in this paper. A power-of-two quantizer is used for the input of the multiplier to reduce the multiplication to at most a simple shift. In spite of its simple implementation, the performance is shown to be comparable to the classical LMS algorithm. A linearized approximation to the quantizer is first derived, followed by the analysis of an exact nonlinear model. The derivation is based on the Gaussian assumption, and the effects of removing the Gaussian assumption are later considered. The roundoff error due to the finite-bit computation is calculated. Computer simulation results are provided to support the analysis.
60 citations