| 截断分层B样条基的Lp稳定性 |
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| 引用本文： | 周健萍,王仁宏,李崇君.截断分层B样条基的Lp稳定性[J].数学研究及应用,2017,37(6):697-709. |
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| 作者姓名： | 周健萍 王仁宏 李崇君 |
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| 作者单位： | 大连理工大学数学科学学院, 辽宁 大连 116024,大连理工大学数学科学学院, 辽宁 大连 116024,大连理工大学数学科学学院, 辽宁 大连 116024 |
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| 基金项目： | 国家自然科学基金(Grant Nos.11290143; 11471066), 民用飞机专项项目(Grant No.MJ-F-2012-04),中央高校基本科研业务费专项资金资助(Grant No.DUT15LK44). |
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| 摘 要： | The truncated hierarchical B-spline basis has been proposed for adaptive data fitting and has already drawn a lot of attention in theory and applications.However the stability with respect to the L_p-norm,1≤p∞,is not clear.In this paper,we consider the L_p stability of the truncated hierarchical B-spline basis,since the L_p stability is useful for curve and surface fitting,especially for least squares fitting.We prove that this basis is weakly L_p stable.This means that the associated constants to be considered in the stability analysis are at most of polynomial growth in the number of the hierarchy depth.
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| 关 键 词： | 分层样条空间 截断分层B样条基 稳定基 基底的条件数 单位分解性 |
| 收稿时间： | 2017/5/25 0:00:00 |
| 修稿时间： | 2017/9/1 0:00:00 |
$L_p$ Stability of the Truncated Hierarchical B-Spline Basis |
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| Jianping ZHOU,Renhong WANG and Chongjun LI.$L_p$ Stability of the Truncated Hierarchical B-Spline Basis[J].Journal of Mathematical Research with Applications,2017,37(6):697-709. |
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| Authors: | Jianping ZHOU Renhong WANG and Chongjun LI |
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| Institution: | Department of Mathematics, Dalian University of Technology, Liaoning 116024, P. R. China,Department of Mathematics, Dalian University of Technology, Liaoning 116024, P. R. China and Department of Mathematics, Dalian University of Technology, Liaoning 116024, P. R. China |
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| Abstract: | The truncated hierarchical B-spline basis has been proposed for adaptive data fitting and has already drawn a lot of attention in theory and applications. However the stability with respect to the $L_p$-norm, $\ 1\leq p < \infty$, is not clear. In this paper, we consider the $L_p$ stability of the truncated hierarchical B-spline basis, since the $L_p$ stability is useful for curve and surface fitting, especially for least squares fitting. We prove that this basis is weakly $L_p$ stable. This means that the associated constants to be considered in the stability analysis are at most of polynomial growth in the number of the hierarchy depth. |
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| Keywords: | hierarchical spline space truncated hierarchical B-spline basis stable basis condition number of basis partition of unity |
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