Computation of best monotone approximations

Author:
James T. Lewis

Journal:
Math. Comp. **26** (1972), 737-747

MSC:
Primary 65D15

MathSciNet review:
0329199

Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: A numerical procedure to compute the best uniform approximation to a given continuous function by algebraic polynomials with nonnegative th derivative is presented and analyzed. The method is based on discretization and linear programming. Several numerical experiments are discussed.

**[1]**E. W. Cheney,*Introduction to approximation theory*, McGraw-Hill Book Co., New York-Toronto, Ont.-London, 1966. MR**0222517****[2]**G. Hadley,*Linear programming*, Addison-Wesley Series in Industrial Management, Addison-Wesley Publishing Co., Inc., Reading, Mass.-London, 1962. MR**0135622****[3]**P. LaFata and J. B. Rosen,*An interactive display for approximation by linear programming*, Comm. ACM**13**(1970), 651–659. MR**0267810****[4]**J. T. Lewis,*Approximation With Convex Constraints*, Doctoral Thesis, Brown University, Providence, R.I., 1969.**[5]**J. T. Lewis,*Approximation With Convex Constraints*, Technical Report #11, University of Rhode Island, Kingston, R.I., 1970. (Submitted for publication.)**[6]**George G. Lorentz and Karl L. Zeller,*Gleichmässige Approximation durch monotone Polynome*, Math. Z.**109**(1969), 87–91 (German). MR**0241852****[7]**G. G. Lorentz and K. L. Zeller,*Monotone approximation by algebraic polynomials*, Trans. Amer. Math. Soc.**149**(1970), 1–18. MR**0285843**, 10.1090/S0002-9947-1970-0285843-5**[8]**J. R. Rice,*Approximation with convex constraints*, J. Soc. Indust. Appl. Math.**11**(1963), 15–32. MR**0159170**

Retrieve articles in *Mathematics of Computation*
with MSC:
65D15

Retrieve articles in all journals with MSC: 65D15

Additional Information

DOI:
https://doi.org/10.1090/S0025-5718-1972-0329199-3

Keywords:
Monotone approximation,
computation of best approximations,
approximation with constraints,
linear programming

Article copyright:
© Copyright 1972
American Mathematical Society