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翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク Backus–Gilbert method ： ウィキペディア英語版 Backus–Gilbert method In mathematics, the Backus–Gilbert method, also known as the optimally localized average (OLA) method is named for its discoverers, geophysicists George E. Backus and James Freeman Gilbert. It is a regularization method for obtaining meaningful solutions to ill-posed inverse problems. Where other regularization methods, such as the frequently used Tikhonov regularization method, seek to impose smoothness constraints on the solution, Backus–Gilbert instead seeks to impose stability constraints, so that the solution would vary as little as possible if the input data were resampled multiple times. In practice, and to the extent that is justified by the data, smoothness results from this. Given a data array X, the basic Backus-Gilbert inverse is: :$\backslash mathbf\_\backslash theta\; =\; \backslash frac\backslash mathbf\_\backslash theta\}^\backslash mathbf\_\backslash theta\}$ where C is the covariance matrix of the data, and G''θ'' is an ''a priori'' constraint representing the source ''θ'' for which a solution is sought. Regularization is implemented by "whitening" the covariance matrix: :$\backslash mathbf^\; =\; \backslash mathbf\; +\; \backslash lambda\; \backslash mathbf$ with C′ replacing C in the equation for H''θ''. Then, :$\backslash mathbf\_\backslash theta^T\backslash mathbf$ is an estimate of the activity of the source ''θ''. ==References== * Backus, G.E., and Gilbert, F. 1968, "The Resolving power of Gross Earth Data," Geophysical Journal of the Royal Astronomical Society, vol. 16, pp. 169–205. * Backus, G.E., and Gilbert, F. 1970, "Uniqueness in the Inversion of inaccurate Gross Earth Data," Philosophical Transactions of the Royal Society of London A, vol. 266, pp. 123–192. * 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Backus–Gilbert method」の詳細全文を読む スポンサード リンク 翻訳と辞書 : 翻訳のためのインターネットリソース Copyright(C) kotoba.ne.jp 1997-2016. All Rights Reserved.