| 希尔伯特空间中的算子样条与一类最优化方法 |
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| 引用本文： | 张新建.希尔伯特空间中的算子样条与一类最优化方法[J].应用数学学报,2011,34(5). |
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| 作者姓名： | 张新建 |
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| 作者单位： | 国防科技大学理学院数学与系统科学系,长沙,410073 |
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| 基金项目： | 国家自然科学基金(10971226)资助项目 |
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| 摘 要： | 在抽象的Hilbert空间中讨论与线性算子和泛函有关的插值和光顺样条的表示和求解.分析了所给算子和泛函的特征对空间结构的影响；引入一种新的内积,证明了新内积的完备性；利用样条在新内积下的投影性质建立了抽象算子样条与一类最优化问题的联系；还指出在本文的基础上可用特征值和特征向量研究抽象算子样条的构造和计算.
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| 关 键 词： | 线性算子 插值与光顺样条 最小范数问题 最优化 |
Operator Splines and a Class of Optimization Method on Hilbert Spaces |
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| ZHANG XINJIAN.Operator Splines and a Class of Optimization Method on Hilbert Spaces[J].Acta Mathematicae Applicatae Sinica,2011,34(5). |
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| Authors: | ZHANG XINJIAN |
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| Institution: | ZHANG XINJIAN (College of Science,National University of Defense and Technology,Changsha 410073) |
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| Abstract: | This paper discusses the expressions and solutions for gerneral interpolating and smoothing splines determined by certain linear operators and linear functionals.The influence of the operators and functionals on the space sconstructivity was analyzed.The relationships between operator splines and a class of optimization problems were established by introduing a new inner product.It is pointed that the operator splines were also related to a matrix and its eigenvectors. |
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| Keywords: | linear operator interpolating and smoothing spline minimum norm problem optimization |
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