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A Single-Pass algorithm for Spectrum Estimation With Fast Convergence

IEEE TRANSACTIONS ON INFORMATION THEORY 2011年第7期57卷 4720-4731页

作者： Xiao, Han Wu, Wei Biao Univ Chicago Dept Stat Chicago IL 60637 USA

We propose a single-pass algorithm for estimating spectral densities of stationary processes. Our algorithm is computationally fast in the sense that, when a new observation arrives, it can provide a real-time update within O (1) computation. The proposed algorithm is probabilistically fast in that, for stationary processes whose auto-covariances decay geometrically, the estimates from the algorithm converge at a rate which is optimal up to a multiplicative logarithmic factor. We also establish asymptotic normality for the recursive estimate. A simulation study is carried out and it confirms the superiority over the classical batched mean estimates.

关键词： Batched mean estimate bias reduction nonparametric estimation physical dependence measure recursive algorithm spectral density stochastic process

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Function-valued Pade-type approximant via E-algorithm and its applications in solving integral equations

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APPLIED MATHEMATICS AND COMPUTATION 2011年第20期217卷 7975-7984页

作者： Gu, Chuanqing Tao, Youtian Shanghai Univ Dept Math Shanghai 200444 Peoples R China Chaohu Coll Dept Math Chaohu 238000 Peoples R China

The function-valued Pade-type approximant (FPTA) was defined in the inner product space [8]. In this work, we choose the coefficients in the Neumann power series to make the inner product with both sides a function-valued system of equations to yield a scalar system. Then we express an FPTA in the determinant form. To avoid the direct computation of the determinants, we present the E-algorithm for FPTA based on the vector-valued E-algorithm given by Brezinski [4]. The method of FPTA via E-algorithm (FPTAVEA) not only includes all previous methods but overcomes their essential difficulties. The numerical experiment for a typical integral equation [1] illustrates that the method of FPTAVEA is simpler and more effective for obtaining the characteristic values and the characteristic functions than all previous methods. In addition, this method is also applicable to other Fredholm integral equations of the second kind without explicit characteristic values and characteristic functions. A corresponding example [12] is given and the numerical result is the same as that in [12]. (C) 2011 Elsevier Inc. All rights reserved.

关键词： Function-valued pade approximant Fredholm integral equation recursive algorithm Characteristic value Characteristic function

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A new bivariate basis representation for Bezier-based triangular patches with quadratic complexity

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COMPUTERS & MATHEMATICS WITH APPLICATIONS 2011年第8期61卷 2292-2295页

作者： Dejdumrong, Natasha King Mongkuts Univ Technol Thonburi Fac Engn Dept Comp Engn Bangkok 10140 Thailand

A new class of bivariate bases for the triangular surface construction, based on quadratic and cubic bivariate Bernstein polynomials, is proposed, by extending a model for the univariate basis with linear complexity. This new basis is recursively expressed by its recurrence formulae which are provided, and its important geometric properties are also described. In addition, a recursive algorithm for calculating a point on this triangular surface is recursively defined in the same manner as in the well known de Casteljau algorithm. The main advantage of this model is its recursive algorithm that is proven to construct a triangular surface of degree n in quadratic computational complexity, O(n(2)). (C) 2010 Elsevier Ltd. All rights reserved.

关键词： Bezier triangular patches Recurrence formulae recursive algorithm Quadratic complexity

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Free knot recursive B-spline for compensation of nonlinear smart sensors

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MEASUREMENT 2011年第5期44卷 888-894页

作者： Wang, Xin Wei, Guo Sun, Jinwei Harbin Inst Technol Dept Automat Testing & Control Harbin 150001 Peoples R China

Compensation of nonlinear smart sensors is an important topic that must always be considered to assure the accuracy of measurement systems. Nowadays, with the advent of microprocessor devices in smart sensors, advanced compensation algorithms can be implemented to improve the accuracy of measurement. In this paper, an inverse modeling methodology based on B-spline is proposed for the compensation of nonlinear smart sensors. To avoid complicated least squares solution of the B-spline, a training algorithm in a recursive form is proposed to reduce the training cost and make the on-chip training of B-spline available. Moreover, the choices of B-spline knots and training points are important designed parameters in this methodology. So the free knot insertion algorithm and training points' selection method are used prior to the training process to improve the accuracy of the inverse models and avoid the under and over fitting. Simulations and results are presented to validate the theoretical expectations. (C) 2011 Elsevier Ltd. All rights reserved.

关键词： Compensation Smart sensor B-spline recursive algorithm Free knot insertion algorithm Training points selection

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recursive estimation for ordered eigenvectors of symmetric matrix with observation noise

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JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS 2011年第2期382卷 822-842页

作者： Chen, Han-Fu Fang, Hai-Tao Zhang, Li-Li Chinese Acad Sci Key Lab Syst & Control Inst Syst Sci AMSS Beijing 100080 Peoples R China

The principal component analysis is to recursively estimate the eigenvectors and the corresponding eigenvalues of a symmetric matrix A based on its noisy observations A(k) = A + N-k, where A is allowed to have arbitrary eigenvalues with multiplicity possibly bigger than one. In the paper the recursive algorithms are proposed and their ordered convergence is established: It is shown that the first algorithm as. converges to a unit eigenvector corresponding to the largest eigenvalue, the second algorithm as. converges to a unit eigenvector corresponding to either the second largest eigenvalue in the case the largest eigenvalue is of single multiplicity or the largest eigenvalue if the multiplicity of the largest eigenvalue is bigger than one, and so on. The convergence rate is also derived. (C) 2011 Elsevier Inc. All rights reserved.

关键词： Principal component analysis (PCA) recursive algorithm Stochastic approximation Ordered convergence Convergence rate

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Support-Predicted Modified-CS for recursive Robust Principal Components' Pursuit

Support-Predicted Modified-CS for Recursive Robust Principal...

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IEEE International Symposium on Information Theory (ISIT)

作者： Qiu, Chenlu Vaswani, Namrata Iowa State Univ Dept Elect & Comp Engn Ames IA 50011 USA

ISBN: (纸本)9781457705953

This work proposes a causal and recursive algorithm for solving the "robust" principal components' analysis problem. We primarily focus on robustness to correlated outliers. In recent work, we proposed a new way to look at this problem and showed how a key part of its solution strategy involves solving a noisy compressive sensing (CS) problem. However, if the support size of the outliers becomes too large, for a given dimension of the current principal components' space, then the number of "measurements" available for CS may become too small. In this work, we show how to address this issue by utilizing the correlation of the outliers to predict their support at the current time;and using this as "partial support knowledge" for solving Modified-CS instead of CS.

关键词： Compressed sensing Correlation Noise Prediction algorithms Principal component analysis Robustness Sparse matrices data compression noisy compressive sensing problem partial support knowledge principal component analysis recursive algorithm robust principal component analysis problem signal reconstruction support-predicted modified-CS problem

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Research and Implementation on the Cloud of Chinese Letter

Research and Implementation on the Cloud of Chinese Letter

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International Conference on Information Science, Automation and Material System

作者： An, Junxiu CUIT Sch Software Engn Chengdu 610025 Peoples R China

ISBN: (纸本)9783037850817

The Chinese word clouds can view the Chinese documents based on users' input or URL web sites, in accordance with the appearing frequency of words in the documents to generate a multi-state performance image, similar to the cloud images, namely, "word cloud". This system first obtains Chinese documents users view, cuts up words to the documents, then counts the frequency of each word, and finally puts the words on the appropriate framework based on the high or low word frequency, showing an effect of "word cloud". This system uses the hash algorithm making the output fonts not overlap, and generates personalized display images of Chinese word clouds, which makes users quickly understand the key information in Chinese documents and presents to users the different visual feelings. With the advent of mass storage of information, people can be more convenient, quick and free search the literature and news facts from the Internet. But searching for a keyword, it can display a broad array of Web Cache. This result wastes a lot of time to read text messages and find the required information. Therefore, how to directly and quickly grasp key information and focus of articles is our research subject. The software based on statistics usually need complex assignment and standard formulas to analysis, formation of highly professional graphic. Commonly used graphical text editor provide users with the weighted ratio and other aspects of visual experience, with strong and practical of research and guidance. But it does not implement the important function that directly convert text to graphics, and to provide readers who search for mass of information with a more intuitive experience, so we come up with the Chinese word cloud system. Chinese word cloud system based on the search engine technology, by utilizing text preprocessing, Chinese word segmentation, statistical word frequency, Java dynamic random display technologies and so on, achieve the display of Chinese word cloud. It

关键词： Chinese word clouds divided word word frequency HashMap hash recursive algorithm

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On Algebraic Approach for MSD Parametric Estimation

On Algebraic Approach for MSD Parametric Estimation

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5th International Conference on Integrated Modeling and Analysis in Applied Control and Automation (IMAACA 2011)

作者： Oueslati, Marouene Thiery, Stephane Gibaru, Olivier Bearee, Richard Moraru, George Arts & Metiers ParisTech INSM Project Team LSIS 8 Bd Louis XIV F-59046 Lille France Ctr Rech INRIA Lille Nord Europe NonA Project Team F-59650 Villeneuve Dascq France

ISBN: (纸本)9788890372476

This article address the identification problem of the natural frequency and the damping ratio of a second order continuous system where the-input is a sinusoidal signal. An algebra based approach for identifying parameters of a Mask Spring Damper (MSD) system its proposed and compared to the Kalman-Bucy filter. The proposed estimator uses the algebraic parametric method in the frequency domain yielding exact formula, when placed in the time domain to identify the unknown parameters. We focus on finding the optimal sinusoidal exciting trajectory which allow to minimize the variance of the identification algorithms. We show that the variance of the estimators issued from the algebraic identification method introduced by Fliess and Sira-Ramirez is less sensitive to the input frequency than the ones obtained by the classical recursive Kalman-Bucy filter. Unlike conventional estimation approach, where the knowledge of the statistical properties of the noise is required, algebraic method is deterministic and non-asymptotic. We show that we don't need to know the variance of the noise so as to perform these algebraic estimators. Moreover, as they are non-asymptotic, we give numerical results where we show that they can be used directly for online estimations without any special setting.

关键词： Parameter estimation recursive algorithm Kalman-Bucy algorithm Forgetting factor Algebraic approach Laplace transform Operational calculus Leibniz formula Integral rules Filtering

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Designing on a Special algorithm of Triple Tree Based on the Analysis of Data Structure

Designing on a Special Algorithm of Triple Tree Based on the...

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International Conference on Advanced Research on Computer Education, Simulation and Modeling

作者： Wang, Min Li, Yunfei Weinan Teachers Univ Dept Comp Sci Weinan Shanxi Peoples R China

ISBN: (纸本)9783642217821

This paper introduces in detail the design and analysis of the algorithm of computing the number of descendant nodes of each node in the triple tree based on analyzing the special storage structures of triple tree. The recursive algorithm description in C is introduced subsequently after the design ideas, the implementation methods, and the concrete steps of the algorithm were given. Finally, the algorithm is evaluated from the two aspects of time complexity and space complexity.

关键词： Triple tree Descendant The triple tree preorder traversal recursive algorithm Time complexity Space complexity

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Study on Degree of Engineering Changes Based on Product Family

Study on Degree of Engineering Changes Based on Product Fami...

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2nd International Conference on Manufacturing Science and Engineering

作者： Zeng, Fuhong Zhou, Lanhua Li, Zerong Panzhihua Univ Panzhihua 617000 Peoples R China

ISBN: (纸本)9783037850398

In order to get the total Degree of Engineering Changes for product family (EDCKBOM), which can help enterprise to select a scheme of Engineering Changes (EC) with a minor EDCKBOM and analyze the type of change propagation for the CE in the product family, the Knowledge-body based on Bill of Material (KBOM) model was built for representing domain-specific knowledge, which was described as trial(GUS, CUS, GUR) and manifested as an AND/OR tree structure. Then, a complete solution system based on recursive algorithm was designed to compute the EDCKBOM. Finally, an example was given, and the approach was proved to be efficient and practical.

关键词： Engineering Changes Bill of Material Change Propagation recursive algorithm

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