Matrix Analysis and Its Applications to Signal Processing
矩阵分析及其在信号处理中的应用
基本信息
- 批准号:02045001
- 负责人:
- 金额:$ 3.58万
- 依托单位:
- 依托单位国家:日本
- 项目类别:Grant-in-Aid for international Scientific Research
- 财政年份:1990
- 资助国家:日本
- 起止时间:1990 至 1992
- 项目状态:已结题
- 来源:
- 关键词:
项目摘要
Matrices appear in almost all fields of mathematics, and their analysis is often a key point of the problems. Matrix theory, however, is now classified into a classical research object and its deeper research is ignored. This research aims at matrix analysis from the standpoint of functional analysis and in relation to graph-combinatorics, and its application to signal processing.(1) T. Ando investigated the Hadamard product as a linear operator on the matrix space, and gave a characterization of its norm with respect to the numerical radius. He succeeded in complete parametrization of all extreme points of some convex set of matrices. On the basis of the idea of majorization he established inequalities complementary to the Golden-Thompson inequalities.(2) From the standpoint of matrix analysis H. Schneider obtained a condition for balancing of a weighted direct graphs. He also established a relation between heights and indices for O-pattern graphs.(3) By a method of combinatorics R. Brualdi succeeded in enumerating the number of self-dual codes. He also obtained a basic result for that all matrices with a common graph are invertible.(4) N. Nagai established a method of construction of digital filters by successive extraction of 2-wire lines.(5) T. Nakazi established a relationship between an extremal problem in the Hardy spaces and a property of a Hankel operator, a generalization of a Hankel matrix.(6) Y. Nakamura extended some extremal problem for matrices in terms of majorization to a problem for a metric in function space and analyzed the structure of its solutions. he also established a formula of norm for a special product of matrices.
矩阵几乎出现在数学的所有领域,而矩阵的分析往往是问题的关键。然而,矩阵理论现在被归为一个经典的研究对象,其更深层次的研究被忽视了。本文从泛函分析的角度,结合图-组合学,研究了矩阵分析及其在信号处理中的应用。(1)T.Ando研究了Hadamard乘积作为矩阵空间上的一个线性算子,并给出了它关于数值半径的范数的刻画。他成功地实现了某些凸矩阵集的所有极点的完全参数化。基于优超的思想,他建立了与Golden-Thompson不等式互补的不等式。(2)从矩阵分析的角度出发,H·施耐德得到了加权有向图平衡的一个条件。他还建立了O-模式图的高度与指数之间的关系。(3)利用组合学方法,R.Brualdi成功地计数了自对偶码的个数。(4)N·Nagai建立了一种通过逐次提取二线线来构造数字滤波器的方法。(5)T·Nakazi建立了Hardy空间中的极值问题与Hankel算子的性质之间的关系,这是Hankel矩阵的推广。(6)Y.Nakamura将一些矩阵的极值问题推广到函数空间中的度量问题,并分析了其解的结构。他还建立了矩阵的一个特殊乘积的范数公式。
项目成果
期刊论文数量(55)
专著数量(0)
科研奖励数量(0)
会议论文数量(0)
专利数量(0)
T.ANDO: "Another approach to the strong Parrott thorem" Journal of Mathematical Analysis and Applications. 171. 125-130 (1992)
T.ANDO:“强帕罗特定理的另一种方法”《数学分析与应用杂志》。
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- 影响因子:0
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R.Brualdi: "Strong Hall matrices" SIAM Jouranl of Matrix Analysis and Applications. (1993)
R.Brualdi:“强霍尔矩阵”SIAM Jouranl 矩阵分析与应用。
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- 影响因子:0
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N.Nagai: "Wave digital filters and orthogonal filters based on extracting two-wire lines" IEEE Transaction on Cirtuits and Systems. 38. 534-539 (1991)
N.Nagai:“基于提取两线线路的波数字滤波器和正交滤波器”IEEE 电路与系统汇刊。
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- 影响因子:0
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T.Ando: "Another approach to the strong Parrot theorem" Journal of Mathematical Analysis and Applications.
T.Ando:“强 Parrot 定理的另一种方法”《数学分析与应用杂志》。
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- 影响因子:0
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T.ANDO: "An alternate variational characterization of matrix Riccati equations" Circuits,Systems and Signal Processing. 9. 223-228 (1990)
T.ANDO:“矩阵 Riccati 方程的替代变分表征”电路、系统和信号处理。
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- 影响因子:0
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ANDO Tsuyoshi其他文献
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Development of a novel precise polycondensation using active site recirculating catalysts
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$ 3.58万 - 项目类别:
Grant-in-Aid for Scientific Research (C)
Development of X-ray sensitizing therapy by precisely designed polymers bearing heavy metals
通过精确设计的含重金属聚合物开发 X 射线增敏疗法
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21300164 - 财政年份:2009
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Grant-in-Aid for Scientific Research (B)
Operator Inequalities and Related Norm Inequalities
算子不等式和相关的范数不等式
- 批准号:
10640183 - 财政年份:1998
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$ 3.58万 - 项目类别:
Grant-in-Aid for Scientific Research (C)
Operator-Theoretic Methods for Matrix Inequalities
矩阵不等式的算子理论方法
- 批准号:
08640230 - 财政年份:1996
- 资助金额:
$ 3.58万 - 项目类别:
Grant-in-Aid for Scientific Research (C)
Research on Inequalities for Operators
算子不等式研究
- 批准号:
60540076 - 财政年份:1985
- 资助金额:
$ 3.58万 - 项目类别:
Grant-in-Aid for General Scientific Research (C)
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