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.

Markov and Bernstein type inequalities for polynomials

1999 ◽  
Vol 1999 (4) ◽  
pp. 156027 ◽  
Author(s):  
NK Govil ◽  
RN Mohapatra
Keyword(s):  
Bernstein Type ◽  
Bernstein Type Inequalities

scholarly journals Bernstein type inequalities for self-normalized martingales with applications

Statistics ◽  
2018 ◽  
Vol 53 (2) ◽  
pp. 245-260
Author(s):  
Xiequan Fan ◽  
Shen Wang
Keyword(s):  
Bernstein Type ◽  
Bernstein Type Inequalities

SOME BERNSTEIN TYPE INEQUALITIES FOR POLYNOMIALS

Analysis ◽  
1985 ◽  
Vol 5 (4) ◽  
Author(s):  
A. Sharma ◽  
V. Singh
Keyword(s):  
Bernstein Type ◽  
Bernstein Type Inequalities
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