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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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TL;DR: In this paper, a linear and nonlinear model for the flow past an obstacle with isolated heating is presented, showing that the low-level lifting is maximized when the flow is along the major axis of the obstacle.
Abstract: The flow past heated topography is examined with both linear and nonlinear models. It is first shown that the forcing of an obstacle with horizontally homogenous surface heating can be approximated by the forcing of an obstacle with surface heating isolated over the obstacle. The small-amplitude flow past an obstacle with isolated heating is then examined with a linear model. Under the linear approximation, the flow response to heated topography is simply the addition of the separate responses to thermal and orographic forcing. These separate responses are first considered individually and then the combined response is examined. Nondimensional parameters are developed that measure the relative importance of thermal and orographic forcing. Nonaxisymmetric forcing is then considered by examining the flow along and across a heated elliptically shaped obstacle. It is shown that the low-level lifting is maximized when the flow is along the major axis of the obstacle. The linear solutions are then test...
42 citations
TL;DR: A class of hp-DG methods that is closely related to other DG schemes, however, combines both p-optimal jump penalty as well as lifting stabilization and it is proved that the resulting error estimates are optimal with respect to both the local element sizes and polynomial degrees.
Abstract: The aim of this paper is to overcome the well-known lack of p-optimality in hp-version discontinuous Galerkin (DG) discretizations for the numerical approximation of linear elliptic problems. For this purpose, we shall present and analyze a class of hp-DG methods that is closely related to other DG schemes, however, combines both p-optimal jump penalty as well as lifting stabilization. We will prove that the resulting error estimates are optimal with respect to both the local element sizes and polynomial degrees.
42 citations
TL;DR: It is shown that this problem is fundamentally different from the other traditional histogram construction algorithms and provided an optimal algorithm that runs in linear time for a small number of buckets and also present results which work for arbitrary weighted maximum error measures.
Abstract: Histograms and Wavelet synopses provide useful tools in query optimization and approximate query answering. Traditional histogram construction algorithms, e.g., V-Optimal, use error measures which are the sums of a suitable function, e.g., square, of the error at each point. Although the best-known algorithms for solving these problems run in quadratic time, a sequence of results have given us a linear time approximation scheme for these algorithms. In recent years, there have been many emerging applications where we are interested in measuring the maximum (absolute or relative) error at a point. We show that this problem is fundamentally different from the other traditional {\rm{non}}{\hbox{-}}\ell_\infty error measures and provide an optimal algorithm that runs in linear time for a small number of buckets. We also present results which work for arbitrary weighted maximum error measures.
42 citations
TL;DR: It is proved that the optimum objective value of any instance lies within the interval [ C ∼ , 6 5 C ∼ ] and this interval is tight, and C ∼ is a trivial lower bound on the optimum Objective value.
42 citations
TL;DR: It is shown that when a nonlinear MIMO system is modeled by a multidimensional Volterra series, periodic noise and random multisines are equivalent excitations to the classical Gaussian noise, allowing for a lower variance of the nonlinear FRF measurements, while the same linear approximation is retrieved.
41 citations