Chebyshev Approximation of Multivariable Functions by the Exponential Expression

Qiiasilinearlzation and primal-dual-eelations of chebyshev-approximation i.

Optimization ◽

10.1080/02331937208842116 ◽

1972 ◽

Vol 3 (6) ◽

pp. 431-451

Author(s):

L. Bittner

Keyword(s):

Chebyshev Approximation ◽

Primal Dual

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Chebyshev approximation to data by geometric elements

Numerical Algorithms ◽

10.1007/bf02108666 ◽

1993 ◽

Vol 5 (10) ◽

pp. 509-522 ◽

Cited By ~ 8

Author(s):

Rudolf Drieschner

Keyword(s):

Chebyshev Approximation ◽

Geometric Elements

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

Journal of Manufacturing Science and Engineering ◽

10.1115/1.2120777 ◽

2005 ◽

Vol 128 (1) ◽

pp. 167-174 ◽

Cited By ~ 13

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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