scholarly journals Kinematic Modeling, Linearization and First-Order Error Analysis

10.5772/5430 ◽  
2008 ◽  
Author(s):  
Andreas Pott ◽  
Manfred Hiller
Keyword(s):  
Error Analysis ◽  
Kinematic Modeling ◽  
Order Error ◽  
First Order

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.

Monte Carlo, Bayesian Monte Carlo and First-Order Error Analysis

2010 ◽  
pp. 53-69 ◽  
Author(s):  
W Warren-Hicks ◽  
S Qian ◽  
J Toll ◽  
D Fischer ◽  
E Fite ◽  
...  
Keyword(s):  
Monte Carlo ◽  
Error Analysis ◽  
Order Error ◽  
First Order ◽  
Bayesian Monte Carlo

scholarly journals Discontinuous Mixed Covolume Methods for Linear Parabolic Integrodifferential Problems

2014 ◽  
Vol 2014 ◽  
pp. 1-8
Author(s):  
Ailing Zhu
Keyword(s):  
Error Analysis ◽  
Error Estimate ◽  
Optimal Order ◽  
Triangular Meshes ◽  
Element Space ◽  
Order Error ◽  
First Order ◽  
Fully Discrete ◽  
Mixed Element

The semidiscrete and fully discrete discontinuous mixed covolume schemes for the linear parabolic integrodifferential problems on triangular meshes are proposed. The error analysis of the semidiscrete and fully discrete discontinuous mixed covolume scheme is presented and the optimal order error estimate in discontinuousH(div)and first-order error estimate inL2are obtained with the lowest order Raviart-Thomas mixed element space.

scholarly journals Discontinuous Mixed Covolume Methods for Parabolic Problems

2014 ◽  
Vol 2014 ◽  
pp. 1-8 ◽  
Author(s):  
Ailing Zhu ◽  
Ziwen Jiang
Keyword(s):  
Error Analysis ◽  
Error Estimate ◽  
Error Estimates ◽  
Parabolic Problems ◽  
Optimal Order ◽  
Order Error ◽  
First Order ◽  
Fully Discrete ◽  
Optimal Order Error Estimates ◽  
Backward Euler

We present the semidiscrete and the backward Euler fully discrete discontinuous mixed covolume schemes for parabolic problems on triangular meshes. We give the error analysis of the discontinuous mixed covolume schemes and obtain optimal order error estimates in discontinuousHdivand first-order error estimate inL2.

Comparison of first-order error analysis and Monte Carlo Simulation in time-dependent lake eutrophication models

1981 ◽  
Vol 17 (4) ◽  
pp. 1051-1059 ◽  
Author(s):  
Donald Scavia ◽  
William F. Powers ◽  
Raymond P. Canale ◽  
Jennie L. Moody
Keyword(s):  
Monte Carlo Simulation ◽  
Monte Carlo ◽  
Error Analysis ◽  
Time Dependent ◽  
Lake Eutrophication ◽  
Order Error ◽  
First Order

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.

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