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Computational methods for least squa...

Su, Zheng.

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Computational methods for least squares problems and clinical trials.

紀錄類型:	書目-電子資源 : Monograph/item
正題名/作者:	Computational methods for least squares problems and clinical trials./
作者:	Su, Zheng.
面頁冊數:	81 p.
附註:	Source: Dissertation Abstracts International, Volume: 66-04, Section: B, page: 2109.
Contained By:	Dissertation Abstracts International66-04B.
標題:	Mathematics. -
電子資源:	http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=3171675
ISBN:	0542084260

Computational methods for least squares problems and clinical trials.
Su, Zheng.

Computational methods for least squares problems and clinical trials. - 81 p.

Source: Dissertation Abstracts International, Volume: 66-04, Section: B, page: 2109.

Thesis (Ph.D.)--Stanford University, 2005.

A practical estimate for the optimal backward errors of linear least squares problems are studied. Dense, sparse, and iterative methods are developed to evaluate the estimate. Numerical results show that the computed estimate of the optimal backward error is very near the true optimal backward error. Algorithms for calculating sequences of upper and lower bounds for the estimate are also developed, based on Gauss quadrature theory. Numerical results show that the bounds converge quickly and are therefore useful in practice. This solves a twenty-five year old problem suggested by Stewart and Wilkinson.

ISBN: 0542084260Subjects--Topical Terms:

515831
Mathematics.

Computational methods for least squares problems and clinical trials.
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245 1 0 $a Computational methods for least squares problems and clinical trials.
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500 $a Source: Dissertation Abstracts International, Volume: 66-04, Section: B, page: 2109.
500 $a Advisers: Tze Leung Lai; Michael Saunders.
502 $a Thesis (Ph.D.)--Stanford University, 2005.
520 $a A practical estimate for the optimal backward errors of linear least squares problems are studied. Dense, sparse, and iterative methods are developed to evaluate the estimate. Numerical results show that the computed estimate of the optimal backward error is very near the true optimal backward error. Algorithms for calculating sequences of upper and lower bounds for the estimate are also developed, based on Gauss quadrature theory. Numerical results show that the bounds converge quickly and are therefore useful in practice. This solves a twenty-five year old problem suggested by Stewart and Wilkinson.
520 $a Test-based approaches are explored to construct confidence intervals in clinical trials with survival time as the primary response. Importance resampling techniques are developed to compute tail probabilities of the tests, thereby reducing the variance of the Monte Carlo estimate of an error probability and thus the number of simulations required to compute sample size and power in the design stage of a clinical trial and to construct confidence intervals from the trial's data.
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