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Least Squares Approximation (least + square_approximation)
Selected AbstractsDetermination of community structure through deconvolution of PLFA-FAME signature of mixed populationBIOTECHNOLOGY & BIOENGINEERING, Issue 3 2007Dipesh K. Dey Abstract Phospholipid fatty acids (PLFAs) as biomarkers are well established in the literature. A general method based on least square approximation (LSA) was developed for the estimation of community structure from the PLFA signature of a mixed population where biomarker PLFA signatures of the component species were known. Fatty acid methyl ester (FAME) standards were used as species analogs and mixture of the standards as representative of the mixed population. The PLFA/FAME signatures were analyzed by gas chromatographic separation, followed by detection in flame ionization detector (GC-FID). The PLFAs in the signature were quantified as relative weight percent of the total PLFA. The PLFA signatures were analyzed by the models to predict community structure of the mixture. The LSA model results were compared with the existing "functional group" approach. Both successfully predicted community structure of mixed population containing completely unrelated species with uncommon PLFAs. For slightest intersection in PLFA signatures of component species, the LSA model produced better results. This was mainly due to inability of the "functional group" approach to distinguish the relative amounts of the common PLFA coming from more than one species. The performance of the LSA model was influenced by errors in the chromatographic analyses. Suppression (or enhancement) of a component's PLFA signature in chromatographic analysis of the mixture, led to underestimation (or overestimation) of the component's proportion in the mixture by the model. In mixtures of closely related species with common PLFAs, the errors in the common components were adjusted across the species by the model. Biotechnol. Bioeng. 2007;96: 409,420. © 2006 Wiley Periodicals, Inc. [source] Forced vibration testing of buildings using the linear shaker seismic simulation (LSSS) testing methodEARTHQUAKE ENGINEERING AND STRUCTURAL DYNAMICS, Issue 7 2005Eunjong Yu Abstract This paper describes the development and numerical verification of a test method to realistically simulate the seismic structural response of full-scale buildings. The result is a new field testing procedure referred to as the linear shaker seismic simulation (LSSS) testing method. This test method uses a linear shaker system in which a mass mounted on the structure is commanded a specified acceleration time history, which in turn induces inertial forces in the structure. The inertia force of the moving mass is transferred as dynamic force excitation to the structure. The key issues associated with the LSSS method are (1) determining for a given ground motion displacement, xg, a linear shaker motion which induces a structural response that matches as closely as possible the response of the building if it had been excited at its base by xg (i.e. the motion transformation problem) and (2) correcting the linear shaker motion from Step (1) to compensate for control,structure interaction effects associated with the fact that linear shaker systems cannot impart perfectly to the structure the specified forcing functions (i.e. the CSI problem). The motion transformation problem is solved using filters that modify xg both in the frequency domain using building transfer functions and in the time domain using a least squares approximation. The CSI problem, which is most important near the modal frequencies of the structural system, is solved for the example of a linear shaker system that is part of the NEES@UCLA equipment site. Copyright © 2005 John Wiley & Sons, Ltd. [source] Comparative study of the least squares approximation of the modified Bessel functionINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN BIOMEDICAL ENGINEERING, Issue 8 2008Jianguo XinArticle first published online: 14 DEC 200 Abstract The least squares problem of the modified Bessel function of the second kind has been considered in this study with the Fourier series, Tchebycheff and Legendre approximation. Numerical evidence shows that the Gibbs phenomenon exists in the approximation with the truncated Fourier series, thus, giving poor convergence results compared with the other polynomial bases. For the latter two cases, the Legendre series perform better than Tchebycheff series in terms of the ,2 norm of the relative errors for each order of the polynomial approximation, and the ratio of the ,2 norm of the relative errors from the corresponding approximation seems to be a constant value of 1.3. Copyright © 2006 John Wiley & Sons, Ltd. [source] The Early History of the Cumulants and the Gram-Charlier SeriesINTERNATIONAL STATISTICAL REVIEW, Issue 2 2000Anders Hald Summary The early history of the Gram-Charlier series is discussed from three points of view: (1) a generalization of Laplace's central limit theorem, (2) a least squares approximation to a continuous function by means of Chebyshev-Hermite polynomials, (3) a generalization of Gauss's normal distribution to a system of skew distributions. Thiele defined the cumulants in terms of the moments, first by a recursion formula and later by an expansion of the logarithm of the moment generating function. He devised a differential operator which adjusts any cumulant to a desired value. His little known 1899 paper in Danish on the properties of the cumulants is translated into English in the Appendix. [source] First-order perturbation analysis of the best rank-(R1, R2, R3) approximation in multilinear algebraJOURNAL OF CHEMOMETRICS, Issue 1 2004Lieven De Lathauwer Abstract In this paper we perform a first-order perturbation analysis of the least squares approximation of a given higher-order tensor by a tensor having prespecified n -mode ranks. This work generalizes the classical first-order perturbation analysis of the matrix singular value decomposition. We will show that there are important differences between the matrix and the higher-order tensor case. We subsequently address (1) the best rank-1 approximation of supersymmetric tensors, (2) the best rank-(R1, R2, R3) approximation of arbitrary tensors and (3) the best rank-(R1, R2, R3) approximation of arbitrary tensors. Copyright © 2004 John Wiley & Sons, Ltd. [source] | ||||||||||