The research of optimality property of a kind of multidimensional wavelet pack bases

2010 ◽  
Author(s):  
Tong-you Zhang
Keyword(s):  
Optimality Property

A New Optimality Property of the Capon Estimator

2017 ◽  
Vol 24 (11) ◽  
pp. 1706-1708 ◽  
Author(s):  
A. Aubry ◽  
V. Carotenuto ◽  
A. De Maio
Keyword(s):  
Optimality Property

Conditional likelihood and power: higher-order asymptotics

1992 ◽  
Vol 438 (1904) ◽  
pp. 433-446 ◽  
Keyword(s):  
Average Power ◽  
Nuisance Parameter ◽  
Second Order ◽  
Conditional Likelihood ◽  
Power Functions ◽  
Third Order ◽  
Contiguous Alternatives ◽  
Higher Order Asymptotics ◽  
Optimality Property ◽  
Lr Test

This paper considers, in the presence of a nuisance parameter, a very large class of tests that includes the conditional and the usual versions of the likelihood ratio (LR), Rao’s and Wald’s tests. Under contiguous alternatives and orthogonal parametrization, the power functions of the conditional and the usual versions of these tests have been compared and, in particular, it is seen that the power functions of the conditional versions, unlike those of the usual versions, are identical, up to the second-order, with the power functions of the corresponding tests with known nuisance parameter. An optimality property of the conditional LR test, in terms of second-order local maximinity, has been established. A test, optimal in the sense of third-order average power under contiguous alternatives, has been proposed. A weaker optimality property of Rao’s test, in terms of third-order average power, has also been indicated.

On the L∞-maximization of the solution of Poisson's equation: Brezis–Gallouet–Wainger type inequalities and applications

2020 ◽  
pp. 1-14
Author(s):  
Davit Harutyunyan ◽  
Hayk Mikayelyan
Keyword(s):  
Modulus Of Continuity ◽  
Poisson’S Equation ◽  
Optimal Estimate ◽  
Poisson's Equation ◽  
Poisson Problem ◽  
Right Hand ◽  
Optimality Property ◽  
Image Position

Abstract For the solution of the Poisson problem with an L∞ right hand side \begin{cases} -\Delta u(x) = f (x) & {\rm in}\ D, \\ u=0 & {\rm on}\ \partial D \end{cases} we derive an optimal estimate of the form \|u\|_\infty\leq \|f\|_\infty \sigma_D(\|f\|_1/\|f\|_\infty), where σ D is a modulus of continuity defined in the interval [0, |D|] and depends only on the domain D. The inequality is optimal for any domain D and for any values of $\|f\|_1$ and $\|f\|_\infty .$ We also show that \sigma_D(t)\leq\sigma_B(t),\text{ for }t\in[0,|D|], where B is a ball and |B| = |D|. Using this optimality property of σ D , we derive Brezis–Galloute–Wainger type inequalities on the L∞ norm of u in terms of the L1 and L∞ norms of f. As an application we derive L∞ − L1 estimates on the k-th Laplace eigenfunction of the domain D.

Tuning continual exploration in reinforcement learning: An optimality property of the Boltzmann strategy

2008 ◽  
Vol 71 (13-15) ◽  
pp. 2507-2520 ◽  
Author(s):  
Youssef Achbany ◽  
François Fouss ◽  
Luh Yen ◽  
Alain Pirotte ◽  
Marco Saerens
Keyword(s):  
Reinforcement Learning ◽  
Optimality Property

scholarly journals From snapshots to modal expansions – bridging low residuals and pure frequencies

2016 ◽  
Vol 802 ◽  
pp. 1-4 ◽  
Author(s):  
Bernd R. Noack
Keyword(s):  
Proper Orthogonal Decomposition ◽  
Orthogonal Decomposition ◽  
Operating Conditions ◽  
Dynamic Mode Decomposition ◽  
Dynamic Mode ◽  
Simple Method ◽  
Reduced Order ◽  
Mode Decomposition ◽  
Optimality Property ◽  
Proper Orthogonal

Data-driven low-order modelling has been enjoying rapid advances in fluid mechanics. Arguably, Sirovich (Q. Appl. Maths, vol. XLV, 1987, pp. 561–571) started these developments with snapshot proper orthogonal decomposition, a particularly simple method. The resulting reduced-order models provide valuable insights into flow physics, allow inexpensive explorations of dynamics and operating conditions, and enable model-based control design. A winning argument for proper orthogonal decomposition (POD) is the optimality property, i.e. the guarantee of the least residual for a given number of modes. The price is unpleasant frequency mixing in the modes which complicates their physical interpretation. In contrast, temporal Fourier modes and dynamic mode decomposition (DMD) provide pure frequency dynamics but lose the orthonormality and optimality property of POD. Sieber et al. (J. Fluid Mech., vol. 792, 2016, pp. 798–828) bridge the least residual and pure frequency behaviour with an ingenious interpolation, called spectral proper orthogonal decomposition (SPOD). This article puts the achievement of the TU Berlin authors in perspective, illustrating the potential of SPOD and the challenges ahead.

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