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- 한국산업응용수학회 JOURNAL OF THE KOREAN SOCIETY FOR INDUSTRIAL AND APPLIED MATHEMATICS Journal of the Korean Society for Industrial and Applied Mathematics Vol.20 No.1
- 발행연도
- 2016.3
- 수록면
- 1 - 15 (15page)
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초록· 키워드
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The continuous analysis, such as smoothness and uniform convergence, for polynomials and polynomial-like functions using differential operators have been studied considerably, parallel to the study of discrete analysis for these functions, using difference operators.
In this work, for the difference operator ∇h with size h ＞ 0, we verify that for an integer m ≥ 0 and a strictly decreasing sequence hn converging to zero, a continuous function f(x) satisfying ∇<SUP>m+1</SUP><SUB>hn</SUB> f(khn) = 0, for every n ≥ 1 and k ∈ Z, turns to be a polynomial of degree ≤ m. The proof used the polynomial convergence, and additionally, we investigated several conditions on convergence to polynomials.
In this work, for the difference operator ∇h with size h ＞ 0, we verify that for an integer m ≥ 0 and a strictly decreasing sequence hn converging to zero, a continuous function f(x) satisfying ∇<SUP>m+1</SUP><SUB>hn</SUB> f(khn) = 0, for every n ≥ 1 and k ∈ Z, turns to be a polynomial of degree ≤ m. The proof used the polynomial convergence, and additionally, we investigated several conditions on convergence to polynomials.
목차
ABSTRACT
1. INTRODUCTION
2. CHARACTERIZATION OF SOLUTIONS TO DIFFERENCE EQUATIONS
3. POINT-WISE CONVERGENCE TO POLYNOMIAL
4. GENERALIZATIONS
REFERENCES
참고문헌 (5)
참고문헌 신청
N. Dyn, Subdivision schemes in computer-aided geometric design, in : W. A. Light (Ed.), Advances in numerical anaysis II: Wavelets, Subdivision Algorithms and Rational Basis Functions, Clarendon Press, Oxford, 1992, 36–104.
J. Warren and H. Weimer, Subdivision Methods for Geometric Design: A Constructive Approach, Morgan Kaufmann, 2001.
E. Kreyszig, Introductory Functional Analysis with Application, John Wiley & Sons, New York, 1978.
P. Davis, Interpolation and Approximation, Blaisdell, New York, 1963.
P. Koch and T. Lyche, Construction of exponential tension B-splines of arbitrary order, in : P. Laurent, A. LeM´ehaut´e, and L. Schumaker (Eds.), Curves and Surfaces, Academic Press, New York, 1991.
J. Warren and H. Weimer, Subdivision Methods for Geometric Design: A Constructive Approach, Morgan Kaufmann, 2001.
E. Kreyszig, Introductory Functional Analysis with Application, John Wiley & Sons, New York, 1978.
P. Davis, Interpolation and Approximation, Blaisdell, New York, 1963.
P. Koch and T. Lyche, Construction of exponential tension B-splines of arbitrary order, in : P. Laurent, A. LeM´ehaut´e, and L. Schumaker (Eds.), Curves and Surfaces, Academic Press, New York, 1991.
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UCI(KEPA) : I410-ECN-0101-2016-410-002764222