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The Back and Forth Nudging algorithm for data assimilation problems : theoretical results on transport equations

Didier Auroux, Maëlle Nodet (2012)

ESAIM: Control, Optimisation and Calculus of Variations

In this paper, we consider the back and forth nudging algorithm that has been introduced for data assimilation purposes. It consists of iteratively and alternately solving forward and backward in time the model equation, with a feedback term to the observations. We consider the case of 1-dimensional transport equations, either viscous or inviscid, linear or not (Burgers’ equation). Our aim is to prove some theoretical results on the convergence, and convergence properties, of this algorithm. We...

The Back and Forth Nudging algorithm for data assimilation problems : theoretical results on transport equations

Didier Auroux, Maëlle Nodet (2012)

ESAIM: Control, Optimisation and Calculus of Variations

In this paper, we consider the back and forth nudging algorithm that has been introduced for data assimilation purposes. It consists of iteratively and alternately solving forward and backward in time the model equation, with a feedback term to the observations. We consider the case of 1-dimensional transport equations, either viscous or inviscid, linear or not (Burgers’ equation). Our aim is to prove some theoretical results on the convergence,...

The BC-method in Multidimensional Spectral Inverse Problem: Theory and Numerical Illustrations

M. I. Belishev, V. Yu. Gotlib, S. A. Ivanov (2010)

ESAIM: Control, Optimisation and Calculus of Variations

This work is devoted to numerical experiments for multidimensional Spectral Inverse Problems. We check the efficiency of the algorithm based on the BC-method, which exploits relations between Boundary Control Theory and Inverse Problems. As a test, the problem for an ellipse is considered. This case is of interest due to the fact that a field of normal geodesics loses regularity on a nontrivial separation set. The main result is that the BC-algorithm works quite successfully in spite of...

The behavior of locally most powerful tests

Marek Omelka (2005)

Kybernetika

The locally most powerful (LMP) tests of the hypothesis H : θ = θ 0 against one-sided as well as two-sided alternatives are compared with several competitive tests, as the likelihood ratio tests, the Wald-type tests and the Rao score tests, for several distribution shapes and for location, shape and vector parameters. A simulation study confirms the importance of the condition of local unbiasedness of the test, and shows that the LMP test can sometimes dominate the other tests only in a very restricted neighborhood...

The best uniform quadratic approximation of circular arcs with high accuracy

Abedallah Rababah (2016)

Open Mathematics

In this article, the issue of the best uniform approximation of circular arcs with parametrically defined polynomial curves is considered. The best uniform approximation of degree 2 to a circular arc is given in explicit form. The approximation is constructed so that the error function is the Chebyshev polynomial of degree 4; the error function equioscillates five times; the approximation order is four. For θ = π/4 arcs (quarter of a circle), the uniform error is 5.5 × 10−3. The numerical examples...

The box method and some error estimation

Mlýnek, Jaroslav (2008)

Programs and Algorithms of Numerical Mathematics

This article focuses its attention on practical use of the box method for solving certain type of partial differential equations. The heat conduction problem of the oil transformer under stationary load is described by this equation. The knowledge of the transformer operating temperature is important for ensuring correct functionality and lifespan of transformer. We consider an elliptic partial differential equation of second order with the Newton boundary condition on a rectangular domain. The...

The Cauchy problem for the homogeneous time-dependent Oseen system in ℝ 3 : spatial decay of the velocity

Paul Deuring (2013)

Mathematica Bohemica

We consider the homogeneous time-dependent Oseen system in the whole space ℝ 3 . The initial data is assumed to behave as O ( | x | - 1 - ϵ ) , and its gradient as O ( | x | - 3 / 2 - ϵ ) , when | x | tends to infinity, where ϵ is a fixed positive number. Then we show that the velocity u decays according to the equation | u ( x , t ) | = O ( | x | - 1 ) , and its spatial gradient ∇ x u decreases with the rate | x | - 3 / 2 , for | x | tending to infinity, uniformly with respect to the time variable t . Since these decay rates are optimal even in the stationary case, they should also be the best possible...

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