论文标题:B_n与L_n中间算子的逼近问题
The Operators" Approximation Problem between L_nf and B_nf
论文作者
论文导师 王晶昕,论文学位 硕士,论文专业 基础数学
论文单位 辽宁师范大学,点击次数 107,论文页数 28页File Size983K
2006-05-01论文网 http://www.lw23.com/lunwen_615914862/
L_n operator;B_n operator;B_n~(k) operator;P_n~ operator;aB_3 operator
Bernstein算子的一致收敛性与Lagrange算子的插值效果历来是人们研究逼近问题时所关注的，但是二者都有自身固有的缺点。B_n~(K)算子和。α_B_n算子是两簇介于B_n和L_n之间的算子，二者兼具了B_n算子和L_n算子的优点，同时弥补了它们的不足之处。 本文研究了B_n~(K)算子和α_B_n算子的逼近性质，给出了B_3~(k)=0，1，2，3)、B_4(k)(k=0，1，2，3，4)、αB_3(α=0，1，2，3，4)的表达式和矩阵形式，并通过实例比较了它们的逼近效果，得出了一般性结论，同时，本文研究了如何用这两类算子来完成满足某些给定条件的多项式曲线的设计，由于最适合应用的多项式是三次多项式，故本文具有一定的实用价值和实践意义。
The approximation problem researchers usually focus on the Bernstein operator"s uniform convergence and the Lagrange operator"s interpolating effect. However, both of them have itself weakness. The B_n~(k) operators and αB_n operators are between B_n and αB_n operators, and they have the virtues of B_n and αB_n operators and are short of their shortcomings.This paper study the approximation properties of B_n~(k) and αB_n, and give the formula and matrix formal of the B_3~(k) (k = 0,1,2,3), B_4~(k) (k = 0,1,2,3,4), aB_3 (α= 0,1,2,3,4). Then we draws a general conclusion by illustrating the approximation effect. This paper also study how to make use of these operators to conduct design of polynomial curve satisfying certain given conditions. Because three orders polynomials are the best fit for applying, this paper has some practical values.
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