Characterization of Local Strict Convexity Preserving Interpolation Methods by C1 Functions
Characterization of Local Strict Convexity Preserving Interpolation Methods by C1 Functions
复制标题
DOI：
10.1006/jath.1994.1030
复制
发表时间：
1994-04
影响因子：
0.9
通讯作者：
J. Carnicer;W. Dahmen
中科院分区：
文献类型：
--
作者：
J. Carnicer;W. Dahmen
研究了一元严格保凸插值问题。证明了对严格凸数据的严格凸Hermite插值总是光滑的，甚至是多项式。此外，两点Hermite严格保凸插值计划既不使用张力参数，也没有额外的结分类根据一些某些理想的属性，如对称性，二次精确性，仿射不变性等的主要结果之一是表征的一组这样的方法作为一个参数家庭的解决方案，某些边值问题。
This paper is concerned with the problem of strict convexity preserving interpolation in one variable. It is shown that a strictly convex Hermite interpolant to strictly convex data can always be chosen smooth and even to be a polynomial. Furthermore, two-point Hermite strict convexity preserving interpolation schemes using neither tension parameters nor additional knots are classified according to a number of certain desirable properties like symmetry, quadratic exactness, affine invariance, etc. One of the main results is the characterization of the set of such methods as a one-parameter family of solutions to certain boundary value problems.