# Characterization theorem of generalized polynomial of best approximation having bounded coefficients

Characterization theorem of generalized polynomial of best approximation having bounded coefficients Let the set of generalized polynomials having bounded coefficients beK={p= \$\$\mathop \Sigma \limits_{j = 1}^n \$\$ α jgj.α j≤α j≤β j,j=1, 2, ...,n}, whereg 1,g 2, ...,g n are linearly independent continuous functions defined on the interval [a, b],α j,β j are extended real numbers satisfyingα j<+∞,β j>-∞, andα j≤β j. Assume thatf is a continuous function defined on a compact setX ⊂ [a, b]. This paper gives the characterization theorem forp being the best uniform approximation tof fromK, and points out that the characterization theorem can be applied in calculating the approximate solution of best approximation tof fromK. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Acta Mathematicae Applicatae Sinica Springer Journals

# Characterization theorem of generalized polynomial of best approximation having bounded coefficients

, Volume 5 (4) – Jul 13, 2005
6 pages      /lp/springer-journals/characterization-theorem-of-generalized-polynomial-of-best-oftMEC6V0H
Publisher
Springer Journals
Copyright © 1989 by Science Press, Beijing, China and Allerton Press, Inc., New York, U.S.A.
Subject
Mathematics; Applications of Mathematics; Math Applications in Computer Science; Theoretical, Mathematical and Computational Physics
ISSN
0168-9673
eISSN
1618-3932
DOI
10.1007/BF02005957
Publisher site
See Article on Publisher Site

### Abstract

Let the set of generalized polynomials having bounded coefficients beK={p= \$\$\mathop \Sigma \limits_{j = 1}^n \$\$ α jgj.α j≤α j≤β j,j=1, 2, ...,n}, whereg 1,g 2, ...,g n are linearly independent continuous functions defined on the interval [a, b],α j,β j are extended real numbers satisfyingα j<+∞,β j>-∞, andα j≤β j. Assume thatf is a continuous function defined on a compact setX ⊂ [a, b]. This paper gives the characterization theorem forp being the best uniform approximation tof fromK, and points out that the characterization theorem can be applied in calculating the approximate solution of best approximation tof fromK.

### Journal

Acta Mathematicae Applicatae SinicaSpringer Journals

Published: Jul 13, 2005

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