Probabilistic Estimation of Matrix Condition Number

2020 ◽  
Vol 246 (6) ◽  
pp. 755-762
Author(s):  
V. S. Antyufeev
Keyword(s):  
Condition Number ◽  
Probabilistic Estimation ◽  
Matrix Condition Number ◽  
Matrix Condition

Tuning the axial singularity method for accurate calculation of potential flow around axisymmetric bodies

1994 ◽  
Vol 98 (976) ◽  
pp. 215-226
Author(s):  
M. F. Zedan
Keyword(s):  
Condition Number ◽  
Intensity Variation ◽  
Axial Line ◽  
Control Points ◽  
Singularity Method ◽  
The Matrix ◽  
Matrix Condition Number ◽  
Order Of Magnitude ◽  
Matrix Condition ◽  
Solution Parameters

Abstract The performance of axial line singularity methods has been investigated systematically for various solution parameters using carefully chosen test cases. The results indicate that increasing the number of elements and using stretched node distribution improves the solution accuracy until the matrix becomes near-singular. The matrix condition number increases with these parameters as well as with the order of intensity variation and profile thickness. For moderate fineness ratios, the linear methods outperform zero-order methods. The linear doublet method performs best with control points at the x-locations of nodes while the source methods perform best with control points mid-way between nodes. The doublet method has a condition number an order of magnitude lower than the source method and generally provides more accurate results and handles a wider range of bodies. With appropriate solution parameters, the method provides excellent accuracy for bodies without slope discontinuity. The smoothing technique proposed recently by Hemsch has been shown to reduce the condition number of the matrix; however it should be used with caution. It is recommended to use it only when the solution is highly oscillatory with a near-singular matrix. A criterion for the optimum value of the smoothing parameter is proposed.

Velocity performance indices for parallel mechanisms with actuation redundancy

Robotica ◽  
2004 ◽  
Vol 22 (2) ◽  
pp. 129-139 ◽  
Author(s):  
Sébastien Krut ◽  
Olivier Company ◽  
François Pierrot
Keyword(s):  
Condition Number ◽  
Parallel Mechanisms ◽  
Performance Indices ◽  
Accurate Representation ◽  
Actuation Redundancy ◽  
Matrix Condition Number ◽  
Matrix Condition

This paper analyses the concept of velocity isotropy for Parallel Mechanisms with Actuation Redundancy (PMAR). The limits of classical indices based on the Jacobean matrix condition number are shown. It is proposed to use either the largest ellipsoid included in the operational polytop, or the operational polytop itself, as better representations of a PMAR capabilities. The polytop is studied because it is actually the accurate representation of a machine capability, while the largest ellipsoid remains similar to the classical tool roboticists are dealing with for decades. Velocity performance indices are proposed, and the ways to compute them efficiently are given.

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