scholarly journals Evaluation of First Order Error Induced by Conservative-Tracer Temperature Approximation for Mixing in Karstic Flow

2015 ◽  
Author(s):  
Philippe Machetel ◽  
◽  
David Yuen ◽  
Keyword(s):  
Order Error ◽  
First Order ◽  
Conservative Tracer

Analysis of a New Mixed Finite Volume Method

2003 ◽  
Vol 3 (1) ◽  
pp. 189-201 ◽  
Author(s):  
Ilya D. Mishev
Keyword(s):  
Finite Volume Method ◽  
Finite Volume ◽  
Elliptic Equations ◽  
Variable Pressure ◽  
Order Error ◽  
First Order ◽  
Scalar Variable ◽  
Volume Method ◽  
Well Posed ◽  
Theoretical Results

AbstractA new mixed finite volume method for elliptic equations with tensor coefficients on rectangular meshes (2 and 3-D) is presented. The implementation of the discretization as a finite volume method for the scalar variable (“pressure”) is derived. The scheme is well suited for heterogeneous and anisotropic media because of the generalized harmonic averaging. It is shown that the method is stable and well posed. First-order error estimates are derived. The theoretical results are confirmed by the presented numerical experiments.

Estimating the error in variational scattering calculations

1978 ◽  
Vol 56 (10) ◽  
pp. 1358-1364 ◽  
Author(s):  
J. W. Darewych ◽  
R. Pooran
Keyword(s):  
Wave Scattering ◽  
Exponential Potential ◽  
S Wave ◽  
Order Error ◽  
Absolute Value ◽  
First Order ◽  
Scattering Phase ◽  
Square Well ◽  
Scattering Phase Shifts ◽  
Made In

We derive bounds to the absolute value of the error that is made in variational estimates of scattering phase shifts. These bounds, like the variational estimates, are second order in 'small' quantities and are, in this respect, an improvement on similar but first-order error bounds derived previously by Bardsley, Gerjuoy, and Sukumar. The s-wave scattering by a square well potential, in the Born approximation, and by an exponential potential, using a many parameter trial function, are used to illustrate the results.

scholarly journals A EUROPEAN OPTION GENERAL FIRST-ORDER ERROR FORMULA

2013 ◽  
Vol 54 (4) ◽  
pp. 248-272 ◽  
Author(s):  
GUILLAUME LEDUC
Keyword(s):  
Random Walks ◽  
European Security ◽  
European Option ◽  
Order Error ◽  
First Order ◽  
Error Formula ◽  
Black Scholes Model ◽  
Black Scholes ◽  
Option Values ◽  
Payoff Functions

AbstractWe study the value of European security derivatives in the Black–Scholes model when the underlying asset $\xi $ is approximated by random walks ${\xi }^{(n)} $. We obtain an explicit error formula, up to a term of order $ \mathcal{O} ({n}^{- 3/ 2} )$, which is valid for general approximating schemes and general payoff functions. We show how this error formula can be used to find random walks ${\xi }^{(n)} $ for which option values converge at a speed of $ \mathcal{O} ({n}^{- 3/ 2} )$.

scholarly journals Robust Calibration of Cameras with Telephoto Lens Using Regularized Least Squares

2014 ◽  
Vol 2014 ◽  
pp. 1-9 ◽  
Author(s):  
Mingpei Liang ◽  
Xinyu Huang ◽  
Chung-Hao Chen ◽  
Gaolin Zheng ◽  
Alade Tokuta
Keyword(s):  
Error Analysis ◽  
Camera Calibration ◽  
Focal Length ◽  
Real Data ◽  
Order Error ◽  
First Order ◽  
Camera Parameters ◽  
The One ◽  
Well Posed ◽  
Telephoto Lens

Cameras with telephoto lens are usually used to recover details of an object that is either small or located far away from the cameras. However, the calibration of this kind of cameras is not as accurate as the one of cameras with short focal lengths that are commonly used in many vision applications. This paper has two contributions. First, we present a first-order error analysis that shows the relation between focal length and estimation uncertainties of camera parameters. To our knowledge, this error analysis with respect to focal length has not been studied in the area of camera calibration. Second, we propose a robust algorithm to calibrate the camera with a long focal length without using additional devices. By adding a regularization term, our algorithm makes the estimation of the image of the absolute conic well posed. As a consequence, the covariance of camera parameters can be reduced greatly. We further used simulations and real data to verify our proposed algorithm and obtained very stable results.

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