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Computation of best monotone approximations
Author:
James T. Lewis
Journal:
Math. Comp. 26 (1972), 737-747
MSC:
Primary 65D15
MathSciNet review:
0329199
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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.
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LaFata and J.
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programming, Comm. ACM 13 (1970), 651–659. MR 0267810
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J. T. Lewis, Approximation With Convex Constraints, Doctoral Thesis, Brown University, Providence, R.I., 1969.
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J. T. Lewis, Approximation With Convex Constraints, Technical Report #11, University of Rhode Island, Kingston, R.I., 1970. (Submitted for publication.)
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George
G. Lorentz and Karl
L. Zeller, Gleichmässige Approximation durch monotone
Polynome, Math. Z. 109 (1969), 87–91 (German).
MR
0241852 (39 #3189)
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G. Lorentz and K.
L. Zeller, Monotone approximation by algebraic
polynomials, Trans. Amer. Math. Soc. 149 (1970), 1–18. MR 0285843
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R. Rice, Approximation with convex constraints, J. Soc.
Indust. Appl. Math. 11 (1963), 15–32. MR 0159170
(28 #2387)
- [1]
- E. W. Cheney, Introduction to Approximation Theory, McGraw-Hill, New York, 1966. MR 36 #5568. MR 0222517 (36:5568)
- [2]
- G. F. Hadley, Linear Programming, Addison-Wesley Series in Industrial Management, Addison-Wesley, Reading, Mass., 1962. MR 24 #B1669. MR 0135622 (24:B1669)
- [3]
- P. LaFata & J. B. Rosen, ``An interactive display for approximation by linear programming,'' Comm. ACM, v. 13, 1970, pp. 651-659. MR 42 #2712. MR 0267810 (42:2712)
- [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]
- G. G. Lorentz & K. L. Zeller, ``Gleichmässige Approximation durch monotone Polynome,'' Math. Z., v. 109, 1969, pp. 87-91. MR 39 #3189. MR 0241852 (39:3189)
- [7]
- G. G. Lorentz & K. L. Zeller, ``Monotone approximation by algebraic polynomials,'' Trans. Amer. Math. Soc., v. 149, 1970, pp. 1-18. MR 0285843 (44:3060)
- [8]
- J. R. Rice, ``Approximation with convex constraints,'' J. Soc. Indust. Appl. Math., v. 11, 1963, pp. 15-32. MR 28 #2387. MR 0159170 (28:2387)
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Additional Information
DOI:
http://dx.doi.org/10.1090/S0025-5718-1972-0329199-3
PII:
S 0025-5718(1972)0329199-3
Keywords:
Monotone approximation,
computation of best approximations,
approximation with constraints,
linear programming
Article copyright:
© Copyright 1972 American Mathematical Society
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