scholarly journals On bernstein type inequalities and a weighted chebyshev approximation problem on ellipses

1990 ◽  
pp. 45-55
Author(s):  
Roland Freund
Keyword(s):  
Chebyshev Approximation ◽  
Approximation Problem ◽  
Bernstein Type ◽  
Bernstein Type Inequalities

Algorithm for Spatial Straightness Evaluation Using Theories of Linear Complex Chebyshev Approximation and Semi-infinite Linear Programming

2005 ◽  
Vol 128 (1) ◽  
pp. 167-174 ◽  
Author(s):  
LiMin Zhu ◽  
Ye Ding ◽  
Han Ding
Keyword(s):  
Linear Programming ◽  
Chebyshev Approximation ◽  
Approximation Problem ◽  
Linear Complex ◽  
Infinite Linear Programming ◽  
Minimum Zone ◽  
Effectiveness And Efficiency ◽  
Primal And Dual ◽  
Straightness Error ◽  
Infinite Linear

This paper presents a novel methodology for evaluating spatial straightness error based on the minimum zone criterion. Spatial straightness evaluation is formulated as a linear complex Chebyshev approximation problem, and then reformulated as a semi-infinite linear programming problem. Both models for the primal and dual programs are developed. An efficient simplex-based algorithm is employed to solve the dual linear program to yield the straightness value. Also a general algebraic criterion for checking the optimality of the solution is proposed. Numerical experiments are given to verify the effectiveness and efficiency of the presented algorithm.

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