scholarly journals Error analysis and improvement of first-order design sensitivity relations

PAMM ◽  
2010 ◽  
Vol 10 (1) ◽  
pp. 583-584
Author(s):  
Daniel Materna ◽  
Franz-Joseph Barthold
Keyword(s):  
Error Analysis ◽  
Design Sensitivity ◽  
First Order

Direct Differentiation Methods for the Design Sensitivity of Multibody Dynamic Systems

1996 ◽  
Author(s):  
Radu Serban ◽  
Jeffrey S. Freeman
Keyword(s):  
Sensitivity Analysis ◽  
Dynamic Systems ◽  
Design Sensitivity ◽  
Differential Algebraic Equations ◽  
Mechanism Analysis ◽  
Algebraic Equations ◽  
First Order ◽  
Direct Differentiation ◽  
Multibody Dynamic ◽  
Standard Techniques

Abstract Methods for formulating the first-order design sensitivity of multibody systems by direct differentiation are presented. These types of systems, when formulated by Euler-Lagrange techniques, are representable using differential-algebraic equations (DAE). The sensitivity analysis methods presented also result in systems of DAE’s which can be solved using standard techniques. Problems with previous direct differentiation sensitivity analysis derivations are highlighted, since they do not result in valid systems of DAE’s. This is shown using the simple pendulum example, which can be analyzed in both ODE and DAE form. Finally, a slider-crank example is used to show application of the method to mechanism analysis.

scholarly journals The Convergence Ball and Error Analysis of the Relaxed Secant Method

2017 ◽  
Vol 2017 ◽  
pp. 1-7
Author(s):  
Rongfei Lin ◽  
Qingbiao Wu ◽  
Minhong Chen ◽  
Lu Liu
Keyword(s):  
Nonlinear Equation ◽  
Error Analysis ◽  
Error Estimate ◽  
Secant Method ◽  
Speed Of Convergence ◽  
Convergence Ball ◽  
Numerical Examples ◽  
Lipschitz Continuous ◽  
First Order ◽  
Nonlinear Equation Systems

A relaxed secant method is proposed. Radius estimate of the convergence ball of the relaxed secant method is attained for the nonlinear equation systems with Lipschitz continuous divided differences of first order. The error estimate is also established with matched convergence order. From the radius and error estimate, the relation between the radius and the speed of convergence is discussed with parameter. At last, some numerical examples are given.

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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