Topic
Inverse trigonometric functions
About: Inverse trigonometric functions is a research topic. Over the lifetime, 854 publications have been published within this topic receiving 11141 citations. The topic is also known as: arcus function & antitrigonometric function.
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TL;DR: In this article , the theoretical properties of Laplace and arctan penalized OLS regression models were studied in the orthonormal design case and in the general design case.
Abstract: Two new non convex penalty functions – Laplace and arctan – were recently introduced in the literature to obtain sparse models for high-dimensional statistical problems. In this article, we study the theoretical properties of Laplace and arctan penalized ordinary least squares linear regression models. We first illustrate the near-unbiasedness of the non zero regression weights obtained by the new penalty functions, in the orthonormal design case. In the general design case, we present theoretical results in two asymptotic settings: (a) the number of features, p fixed, but the sample size, n→∞, and (b) both n and p tend to infinity. The theoretical results shed light onto the differences between the solutions based on the new penalty functions and those based on existing convex and non convex Bridge penalty functions. Our theory also shows that both Laplace and arctan penalties satisfy the oracle property. Finally, we also present results from a brief simulations study illustrating the performance of Laplace and arctan penalties based on the gradient descent optimization algorithm.
TL;DR: In this paper , the approximation of Bessel functions with finite sums of trigonometric functions was considered, in the light of recent evaluations of Neumann-Bessel series with trigonometrical coefficients.
Abstract: I reconsider the approximation of Bessel functions with finite sums of trigonometric functions, in the light of recent evaluations of Neumann-Bessel series with trigonometric coefficients. A proper choice of the angle allows for
an efficient choice of the trigonometric sum. Based on these series, I also obtain straightforward non-standard
evaluations of new parametric sums with powers of cosine and sine functions.
TL;DR: In this paper , a single rotating polarizer system was proposed for extracting the optical rotation angle of optically active media using an arctangent method or lock-in algorithm.
TL;DR: In this article, a series of trigonometric functions is presented.Click on the link to view the abstract. But the authors do not discuss the relation between these functions and the series of functions.
Abstract: Click on the link to view the abstract. Keywords: Series of trigonometric functions Quaestiones Mathematicae 31(2008), 375–378