Computation of best one-sided approximation

Author:
James T. Lewis

Journal:
Math. Comp. **24** (1970), 529-536

MSC:
Primary 65.20; Secondary 41.00

MathSciNet review:
0273780

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Abstract | References | Similar Articles | Additional Information

Abstract: A computational procedure based on linear programming is presented for finding the best one-sided approximation to a given function. A theorem which ensures that the computational procedure yields approximations which converge to the best approximation is proved. Some numerical examples are discussed.

**[1]**R. Bojanić and R. DeVore,*On polynomials of best one sided approximation*, Enseignement Math. (2)**12**(1966), 139–164. MR**0213790****[2]**Philip J. Davis,*Interpolation and approximation*, Blaisdell Publishing Co. Ginn and Co. New York-Toronto-London, 1963. MR**0157156****[3]**Ronald DeVore,*One-sided approximation of functions*, J. Approximation Theory**1**(1968), no. 1, 11–25. MR**0230018****[4]**Saul I. Gass,*Linear programming: methods and applications*, McGraw-Hill Book Co., Inc., New York-Toronto-London, 1958. MR**0096554****[5]**G. Hadley,*Linear programming*, Addison-Wesley Series in Industrial Management, Addison-Wesley Publishing Co., Inc., Reading, Mass.-London, 1962. MR**0135622****[6]**W. Kammerer,*Optimal Approximations of Functions*:*One-Sided Approximation and Extrema Preserving Approximations*, Doctoral Thesis, Univ. of Wisconsin, Madison, Wisconsin, 1959.**[7]**P.-J. Laurent,*Approximation uniforme de fonctions continues sur un compact avec contraintes de type inégalité*, Rev. Française Informat. Recherche Opérationnelle**1**(1967), no. 5, 81–95 (French). MR**0226265****[8]**J. T. Lewis,*Approximation with Convex Constraints*, Doctoral thesis, Brown University, Providence, R. I., 1969.**[9]**T. S. Motzkin and J. L. Walsh,*Least 𝑝th power polynomials on a finite point set*, Trans. Amer. Math. Soc.**83**(1956), 371–396. MR**0081991**, 10.1090/S0002-9947-1956-0081991-6**[10]**Philip Rabinowitz,*Applications of linear programming to numerical analysis*, SIAM Rev.**10**(1968), 121–159. MR**0226810****[11]**Theodore J. Rivlin,*An introduction to the approximation of functions*, Blaisdell Publishing Co. Ginn and Co., Waltham, Mass.-Toronto, Ont.-London, 1969. MR**0249885**

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Additional Information

DOI:
https://doi.org/10.1090/S0025-5718-1970-0273780-5

Keywords:
One-sided approximation,
approximation,
convex constraints,
computation of best approximation,
linear programming

Article copyright:
© Copyright 1970
American Mathematical Society