This paper describes new high order algorithms in the least-squares problem with harmonic regressor and SDD (Strictly Diagonally Dominant) information matrix. Estimation accuracy and the number of steps to achieve thi...
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ISBN:
(纸本)9781467360906
This paper describes new high order algorithms in the least-squares problem with harmonic regressor and SDD (Strictly Diagonally Dominant) information matrix. Estimation accuracy and the number of steps to achieve this accuracy are controllable in these algorithms. Simplified forms of the highorder matrix inversion algorithms and the high order algorithms of direct calculation of the parameter vector are found. The algorithms are presented as recursive procedures driven by estimation errors multiplied by the gain matrices, which can be seen as preconditioners. A simple and recursive (with respect to order) algorithm for update of the gain matrix, which is associated with Neumann series is found. It is shown that the limiting form of the algorithm (algorithm of infinite order) provides perfect estimation. A new form of the gain matrix is also a basis for unification method of high order algorithms. New combined and fast convergent high order algorithms of recursive matrix inversion and algorithms of direct calculation of the parameter vector are presented. The stability of algorithms is proved and explicit transient bound on estimation error is calculated. New algorithms are simple, fast and robust with respect to round-off error accumulation.
This paper describes new high order algorithms in the least-squares problem with harmonic regressor and SDD (Strictly Diagonally Dominant) information matrix. Estimation accuracy and the number of steps to achieve thi...
详细信息
ISBN:
(纸本)9781467360890
This paper describes new high order algorithms in the least-squares problem with harmonic regressor and SDD (Strictly Diagonally Dominant) information matrix. Estimation accuracy and the number of steps to achieve this accuracy are controllable in these algorithms. Simplified forms of the highorder matrix inversion algorithms and the high order algorithms of direct calculation of the parameter vector are found. The algorithms are presented as recursive procedures driven by estimation errors multiplied by the gain matrices, which can be seen as preconditioners. A simple and recursive (with respect to order) algorithm for update of the gain matrix, which is associated with Neumann series is found. It is shown that the limiting form of the algorithm (algorithm of infinite order) provides perfect estimation. A new form of the gain matrix is also a basis for unification method of high order algorithms. New combined and fast convergent high order algorithms of recursive matrix inversion and algorithms of direct calculation of the parameter vector are presented. The stability of algorithms is proved and explicit transient bound on estimation error is calculated. New algorithms are simple, fast and robust with respect to round-off error accumulation.
A new robust and computationally efficient solution to least-squares problem in the presence of round-off errors is proposed. The properties of a harmonic regressor are utilized for design of new combined algorithms o...
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ISBN:
(纸本)9781467357173
A new robust and computationally efficient solution to least-squares problem in the presence of round-off errors is proposed. The properties of a harmonic regressor are utilized for design of new combined algorithms of direct calculation of the parameter vector. In addition, an explicit transient bound for estimation error is derived for classical recursive least-squares (RLS) algorithm using Lyapunov function method. Different initialization techniques of the gain matrix are proposed as an extension of RLS algorithm. All the results are illustrated by simulations.
A new robust and computationally efficient solution to least-squares problem in the presence of round-off errors is proposed. The properties of a harmonic regressor are utilized for design of new combined algorithms o...
详细信息
ISBN:
(纸本)9781467357159
A new robust and computationally efficient solution to least-squares problem in the presence of round-off errors is proposed. The properties of a harmonic regressor are utilized for design of new combined algorithms of direct calculation of the parameter vector. In addition, an explicit transient bound for estimation error is derived for classical recursive least-squares (RLS) algorithm using Lyapunov function method. Different initialization techniques of the gain matrix are proposed as an extension of RLS algorithm. All the results are illustrated by simulations.
high dimensional data analysis has gained widespread acceptance with the rapid development of analytical instruments and experimental techniques. Benefiting from the second order advantage, highorder chemometric algo...
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high dimensional data analysis has gained widespread acceptance with the rapid development of analytical instruments and experimental techniques. Benefiting from the second order advantage, highorder chemometric algorithms have shown a great ability to match the nature of data and extract the latent components from the data. In this study, multiway principal component analysis (NPCA), parallel factor analysis (PARAFAC) and alternating trilinear decomposition (ATLD) were employed, respectively, to extract the information from temperature dependent near infrared (NIR) spectra of alcohol aqueous solutions. The variations of the structure induced by temperature and concentration in the solutions were analyzed by the three algorithms. Spectral features can be observed from the loadings obtained by NPCA, which explain the maximum variances. Spectral profiles computed by PARAFAC and ATLD contain the spectral information of the components. The former prefers to show the information of ethanol, water and ethanol water cluster, while the latter opts for describing the information of the ethanol and different water clusters in the solution. However, all the three algorithms are able to capture the quantitative information from the spectra. Therefore, highorder chemometric algorithms may provide powerful tools for analyzing temperature dependent NIR spectra to obtain the structural and quantitative information of the aqueous solutions.
An efficient higher-order finite difference algorithm is presented in this article for solving systems of two-dimensional reaction-diffusion equations with nonlinear reaction terms. The method is fourth-order accurate...
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An efficient higher-order finite difference algorithm is presented in this article for solving systems of two-dimensional reaction-diffusion equations with nonlinear reaction terms. The method is fourth-order accurate in both the temporal and spatial dimensions. It requires only a regular five-point difference stencil similar to that used in the standard second-order algorithm, such as the Crank-Nicolson algorithm. The Pade approximation and Richardson extrapolation are used to achieve high-order accuracy in the spatial and temporal dimensions, respectively. Numerical examples are presented to demonstrate the efficiency and accuracy of the new algorithm. (C) 2002 Wiley Periodicals, Inc.
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