Using spectral decomposition of a matrix and multi-scale representation of spectral as well as multi-scale transform of a signal, a quasi multi-scale PCA method is proposed to analyze the reason why multi-scale detection method does well than single scale method.
基于矩阵的谱分解、信号的多尺度变换及谱的多尺度表示，提出一种拟多尺度主元分析方法，从机理上分析了多尺度检测方法优于传统单尺度检测方法的内在原因。
The main contents and results of the research in this dissertation are summarized as follows:(1)The application research of 46 kinds of the spatial-temporal statistical analyses The dissertation discusses the definitions, functions and applications of 46 kinds of spatial-temporal statistical analyses of the Web-MAGIS:the basic statistics, Buffer Analysis, Empirical Orthogonal Function, Empirical Mode Decomposition, Singular Value Decomposition, Powerful Spectrum, Fast Fourier Transformation, Cross-spectral Analysis, Harmonic Analysis, Spectral Entropy Analysis, Wavelet Analysis, Singular Spectrum Analysis, Trend Analysis, Cluster Analysis, Factor Analysis, Discriminant Analysis, Two-dimensional Fourier Analysis, Multivariate Regress Analysis, Canonical Correlation Analysis, Anti-distance Weighting Interpolation, Kriging Interpolation and so on.
论文的从要工做及所取得的研讨解果如上：(1)46类时空统计剖析的当用研讨阐述了Web-MAGIS外基本统计、缓冲区剖析、经验反交函数开解、经验模式、偶怪值开解、功率谱、Fast Fourier Transformation、交叉谱剖析、协调剖析、熵谱、大波剖析、偶怪谱剖析、趋背剖析、集类剖析、果女剖析、判别剖析、两维傅外叶剖析、长元归归、典型相闭剖析、反距合权沉拔值、克外金拔值等46类时空统计剖析的含义、功能、当用范围等。
It is known that the spectral decomposition estimate has many properties.
我们知道，由谱分解方法得到的参数的估计有很多优良的性质。
For instance, the spectral image compression algorithm [5] is based on the singular value decomposition.
例如，光谱图像压缩算法[5]是基于奇异值分解。
In this paper, some seismic attributes that include seismic waveform classification, spectral decomposition, 3D visual, and AVO characteristics were extracted from pre-stack and post-stack seismic data that include far, near offset and full offset stacked seismic data. By integrating above information, the question of heterogeneity was solved to a certain extent and the reservoir and gas-bearing were predicated. At last, the pitfalls which occur in the application of seismic attribute are summarized.
利用保真处理的三维地震数据体，进行叠前及叠后地震资料的地震属性、波形分类、频谱分解处理和三维可视化、AVO远近道对比研究，并综合上述研究成果进行岩性与含气砂体的横向预测，较好地解决了有效储层分布及含气有利区块分布的非均质性问题，同时指出了研究过程中使用地震属性时应注意的问题。
But its new estimate is differ from the spectral decomposition estimate of the covariance matrix. At the same time, we prove the property that the risk function of the new estimate of the covariance matrix is less than its spectral decomposition estimate, ANOVAE and MINQUE under Stein loss in some models.
其次，我们给出了观测向量协方差阵特征根及方差分量的压缩估计，并证明了这些新估计的一些统计性质；另外，我们还证明了观测向量协方差阵的特征根及方差分量的压缩估计在均方误差意义下优于其谱分解估计。
With the aid of the spectral decomposition and finite expression formula of matrix we can compute matrix function.
利用矩阵函数的谱分解与有限表示形式计算矩阵函数。
The K, F, R, M and some other absorption bands were reasonably resolved from the absorption spectra of the colored crystals, and their spectral parameters were accurately determined by using spectral decomposition.
用解谱的方法，分别从着色氯化钾和溴化钾晶体吸收光谱中合理地分解出K、F、R、M和一些其它吸收带，并精确确定这些吸收带的光谱参数。
We compare the spectral decomposition estimate by the analysis of variance estimate in the linear mixed model with two variance components.
考虑含有两个方差分量矩阵的多元混合模型，将一元混合模型下的谱分解估计推广到多元模型下。
The proper orthogonal decomposition (POD) - based spectral representation method is used to digitally simulate wind fields around bridges with wind passage effects.
将特征正交分解型谱表示法运用于模拟具有桥塔风效应的桥梁风场中。
This paper also introduces the calculating of matrix power series with the generalized spectral decomposition.
介绍了广义谱分解在计算矩阵幂级数中的应用。
Application of spectral decomposition for fine seismic structural interpretation in coalfield and gas-bearing property predication of coal seam
频谱分解技术在煤田精细构造解释及煤含气性预测中的应用
Based on up-and down-going wave decomposition and elastic wave power reciprocity theorem, this paper derives, in the lateral velocity varying case, linear prediction operator's expression and the generalized spectral factorization equation for reflection dataset.
本文基于上下行波分解及弹性波互易定理，导出横向变速介质条件下线性预测算子的表达式和反射数据的广义谱分解方程。
Obtaining the instantaneous seismic wavelet through the spectral decomposition to the seismic data, thus get the absorption coefficient by fitting the attenuation curve of low and high frequency part of the instantaneous wavelet spectrum to realize the reservoir fluid identification.
通过对地震资料进行瞬时谱分解，求取瞬时地震子波，然后分别拟合子波低频段和高频段的衰减曲线求取吸收系数，实现对储层流体的识别。
It is operator matrix, the convexity and concavity of function, the spectral decomposition of operator and functional calculus that the author is using to generalize some classical inequalities and then to give series of important operator inequalities and norm inequalities.
本文作者就是借助算子矩阵、函数的凸性和凹性、谱分解、函数演算等为工具，将许多经典的不等式加以推广并给出一系列重要的算子不等式与范数不等式。
In the present paper, integrable decomposition is made for the soliton equations generated from the spectral problem with 3 × 3 matrix coefficients.
本文研究3×3谱问题产生的孤子方程的可积分解。
Yamamoto presented a frequency domain decomposition method called Coarse Graining Spectral Analysis (CGSA).
因此有人根据1／f成份的特点提出了所谓粗粒化谱分析的频域分解方法。
Spectral analysis of the domain boundary operator contained in preconditioners for elliptic problems by domain decomposition
基于区域分解的椭圆型问题预处理器中区域边界算子的谱分析
The properties of the polynomial conjugate operator and the necessary and sufficient conditions for the regular valve to exist are studied by using spectral decomposition and properties of normal operator in Hilbert space.
应用希尔伯特空间上正规算子的概念，性质和谱分解定理，研究了多项式共轭算子的性质及正则值存在的充要条件。
By spectral decomposition of a Hermitian operator and functional calculus, some important norm inequalities on complex Hilbert space are obtained.
该文给出了它的另一种证明，同时应用算子分解和函数演算，证明了复Hilbert空间上的自伴算子的几个重要范数不等式。