A fast algorithm for linear complex Chebyshev approximation

1990 ◽  
pp. 265-273 ◽  
Author(s):  
P. T. P. Tang
Keyword(s):  
Fast Algorithm ◽  
Chebyshev Approximation ◽  
Linear Complex

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.

Fast algorithm for the three-dimensional Poisson equation in infinite domains

2020 ◽  
Author(s):  
Chunxiong Zheng ◽  
Xiang Ma
Keyword(s):  
Poisson Equation ◽  
Fast Algorithm ◽  
Root Function ◽  
Computational Cost ◽  
Three Dimensional ◽  
Chebyshev Approximation ◽  
Laplacian Operator ◽  
Square Root ◽  
Infinite Domain ◽  
Infinite Domains

Abstract This paper is concerned with a fast finite element method for the three-dimensional Poisson equation in infinite domains. Both the exterior problem and the strip-tail problem are considered. Exact Dirichlet-to-Neumann (DtN)-type artificial boundary conditions (ABCs) are derived to reduce the original infinite-domain problems to suitable truncated-domain problems. Based on the best relative Chebyshev approximation for the square-root function, a fast algorithm is developed to approximate exact ABCs. One remarkable advantage is that one need not compute the full eigensystem associated with the surface Laplacian operator on artificial boundaries. In addition, compared with the modal expansion method and the method based on Pad$\acute{\textrm{e}}$ approximation for the square-root function, the computational cost of the DtN mapping is further reduced. An error analysis is performed and numerical examples are presented to demonstrate the efficiency of the proposed method.

scholarly journals A fast algorithm for linear complex Chebyshev approximations

1988 ◽  
Vol 51 (184) ◽  
pp. 721-721 ◽  
Author(s):  
Ping Tak Peter Tang
Keyword(s):  
Fast Algorithm ◽  
Linear Complex

Optimization of Perfect Reconstruction Cosine-Modulated Filter Banks: Fast Algorithm

2001 ◽  
Vol 56 (12) ◽  
pp. 8 ◽  
Author(s):  
Oscar G. Ibarra-Manzano ◽  
Yuriy V. Shkvarko ◽  
Rene Jaime-Rivas ◽  
Jose A. Andrade-Lucio ◽  
Gordana Jovanovic-Dolecek
Keyword(s):  
Fast Algorithm ◽  
Filter Banks ◽  
Perfect Reconstruction

Fast algorithm for prediction of satellite imaging and communication opportunities

2001 ◽  
Vol 24 (6) ◽  
pp. 1118-1124
Author(s):  
Yan Mai ◽  
Philip Palmer
Keyword(s):  
Fast Algorithm ◽  
Satellite Imaging
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