The Rate of Convergence for Linear Shape-Preserving Algorithms
Dmitry Boytsov; Sergei Sidorov
Concrete Operators (2015)
- Volume: 2, Issue: 1, page 139-145, electronic only
- ISSN: 2299-3282
Access Full Article
topAbstract
topHow to cite
topDmitry Boytsov, and Sergei Sidorov. "The Rate of Convergence for Linear Shape-Preserving Algorithms." Concrete Operators 2.1 (2015): 139-145, electronic only. <http://eudml.org/doc/275975>.
@article{DmitryBoytsov2015,
abstract = {We prove some results which give explicit methods for determining an upper bound for the rate of approximation by means of operators preserving a cone. Thenwe obtain some quantitative results on the rate of convergence for some sequences of linear shape-preserving operators.},
author = {Dmitry Boytsov, Sergei Sidorov},
journal = {Concrete Operators},
keywords = {shape-preserving approximation; Korovkin-type results; degree of approximation},
language = {eng},
number = {1},
pages = {139-145, electronic only},
title = {The Rate of Convergence for Linear Shape-Preserving Algorithms},
url = {http://eudml.org/doc/275975},
volume = {2},
year = {2015},
}
TY - JOUR
AU - Dmitry Boytsov
AU - Sergei Sidorov
TI - The Rate of Convergence for Linear Shape-Preserving Algorithms
JO - Concrete Operators
PY - 2015
VL - 2
IS - 1
SP - 139
EP - 145, electronic only
AB - We prove some results which give explicit methods for determining an upper bound for the rate of approximation by means of operators preserving a cone. Thenwe obtain some quantitative results on the rate of convergence for some sequences of linear shape-preserving operators.
LA - eng
KW - shape-preserving approximation; Korovkin-type results; degree of approximation
UR - http://eudml.org/doc/275975
ER -
References
top- [1] Barnabas B., Coroianu L., Gal Sorin G., Approximation and shape preserving properties of the Bernstein operator of maxproduct kind, Int. J. of Math. and Math., 2009, Article ID 590589, 1–26 Zbl1188.41016
- [2] Boytsov D. I., Sidorov S. P., Linear approximation method preserving k-monotonicity, Siberian electronic mathematical reports, 2015, 12, 21–27
- [3] Cárdenas-Morales D., Garrancho P., Rasa I., Bernstein-type operators which preserve polynomials, Comput. Math. Appl., 2011, 62, 158–163 [WoS] Zbl1228.41019
- [4] Cárdenas-Morales D., Muñoz-Delgado F. J., Improving certain Bernstein-type approximation processes, Mathematics and Computers in Simulation, 2008, 77, 170–178 Zbl1142.41302
- [5] Cárdenas-Morales D., Muñoz-Delgado F. J., Garrancho P., Shape preserving approximation by Bernstein-type operators which fix polynomials, Applied Mathematics and Computation, 2006, 182, 1615–1622 Zbl1136.65018
- [6] Floater M. S., On the convergence of derivatives of Bernstein approximation, J. Approx. Theory, 2005, 134, 130–135 [Crossref] Zbl1068.41010
- [7] Gal Sorin G., Shape-Preserving Approximation by Real and Complex Polynomials, Springer, 2008 Zbl1154.41002
- [8] Gonska H. H., Quantitative Korovkin type theorems on simultaneous approximation, Mathematische Zeitschrift, 1984, 186 (3), 419–433 Zbl0523.41013
- [9] Knoop H.-B., Pottinger P., Ein satz vom Korovkin-typ fur Ck raume, Math. Z., 1976, 148, 23–32 Zbl0322.41016
- [10] Kopotun K. A., Leviatan D., Prymak A., Shevchuk I. A., Uniform and pointwise shape preserving approximation by algebraic polynomials, Surveys in Approximation Theory, 2011, 6, 24–74 Zbl1296.41001
- [11] Kopotun K., Shadrin A., On k-monotone approximation by free knot splines, SIAM J. Math. Anal., 2003, 34, 901–924 Zbl1031.41007
- [12] Korovkin P. P., On the order of approximation of functions by linear positive operators, Dokl. Akad. Nauk SSSR, 1957, 114 (6), 1158–1161 (in Russian) Zbl0084.06104
- [13] Kvasov B. I., Methods of shape preserving spline approximation, Singapore: World Scientific Publ. Co. Pte. Ltd., 2000 Zbl0960.41001
- [14] Muñoz-Delgado F. J., Cárdenas-Morales D., Almost convexity and quantitative Korovkin type results, Appl.Math. Lett., 1998, 94 (4), 105–108 [Crossref] Zbl0942.41013
- [15] Muñoz-Delgado F. J., Ramírez-González V., Cárdenas-Morales D., Qualitative Korovkin-type results on conservative approximation, J. Approx. Theory, 1998, 94, 144–159 Zbl0911.41015
- [16] Pál J., Approksimation of konvekse funktioner ved konvekse polynomier, Mat. Tidsskrift, 1925, B, 60–65 Zbl51.0210.02
- [17] Popoviciu T., About the Best Polynomial Approximation of Continuous Functions. Mathematical Monography. Sect. Mat. Univ. Cluj., 1937, fasc. III, (in Romanian) Zbl63.0959.03
- [18] Pˇaltˇanea R., A generalization of Kantorovich operators and a shape-preserving property of Bernstein operators, Bulletin of the Transilvania University of Brasov, Series III: Mathematics, Informatics, Physics, 2012, 5 (54), 65–68
- [19] Shisha O., Mond B., The degree of convergence of linear positive operators, Proc. Nat. Acad. Sci. U.S.A., 1968, 60, 1196– 1200 Zbl0164.07102
- [20] Sidorov S. P., Negative property of shape preserving finite-dimensional linear operators, Appl.Math. Lett., 2003, 16 (2), 257– 261 [Crossref] Zbl1062.41018
- [21] Sidorov S. P., Linear relative n-widths for linear operators preserving an intersection of cones, Int. J. of Math. and Math., 2014, Article ID 409219, 1–7 Zbl1310.41013
- [22] Sidorov S.P., On the order of approximation by linear shape-preserving operators of finite rank, East Journal on Approximations, 2001, 7 (1), 1–8 Zbl1085.41508
NotesEmbed ?
topTo embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.