Spectrum unfolding by the least-squares methods

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The method of least squares is briefly reviewed, and the conditions under which it may be used are stated. From this analysis, a least-squares approach to the solution of the dosimetry neutron spectrum unfolding problem is introduced. The mathematical solution to this least-squares problem is derived from the general solution. The existence of this solution is analyzed in some detail. A chi/sup 2/-test is derived for the consistency of the input data which does not require the solution to be obtained first. The fact that the problem is technically nonlinear, but should be treated in general as a linear one, ... continued below

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Pages: 47

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Perey, F.G. January 1, 1977.

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Description

The method of least squares is briefly reviewed, and the conditions under which it may be used are stated. From this analysis, a least-squares approach to the solution of the dosimetry neutron spectrum unfolding problem is introduced. The mathematical solution to this least-squares problem is derived from the general solution. The existence of this solution is analyzed in some detail. A chi/sup 2/-test is derived for the consistency of the input data which does not require the solution to be obtained first. The fact that the problem is technically nonlinear, but should be treated in general as a linear one, is argued. Therefore, the solution should not be obtained by iteration. Two interpretations are made for the solution of the code STAY'SL, which solves this least-squares problem. The relationship of the solution to this least-squares problem to those obtained currently by other methods of solving the dosimetry neutron spectrum unfolding problem is extensively discussed. It is shown that the least-squares method does not require more input information than would be needed by current methods in order to estimate the uncertainties in their solutions. From this discussion it is concluded that the proposed least-squares method does provide the best complete solution, with uncertainties, to the problem as it is understood now. Finally, some implications of this method are mentioned regarding future work required in order to exploit its potential fully.

Physical Description

Pages: 47

Notes

Dep. NTIS, PC A03/MF A01.

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  • Meeting on current status of neutron spectrum unfolding, Oak Ridge, TN, USA, 10 Oct 1977

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  • Report No.: CONF-771096-1
  • Grant Number: W-7405-ENG-26
  • Office of Scientific & Technical Information Report Number: 5207996
  • Archival Resource Key: ark:/67531/metadc1057797

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Office of Scientific & Technical Information Technical Reports

Reports, articles and other documents harvested from the Office of Scientific and Technical Information.

Office of Scientific and Technical Information (OSTI) is the Department of Energy (DOE) office that collects, preserves, and disseminates DOE-sponsored research and development (R&D) results that are the outcomes of R&D projects or other funded activities at DOE labs and facilities nationwide and grantees at universities and other institutions.

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  • January 1, 1977

Added to The UNT Digital Library

  • Jan. 22, 2018, 7:23 a.m.

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  • Feb. 1, 2018, 6:14 p.m.

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Perey, F.G. Spectrum unfolding by the least-squares methods, article, January 1, 1977; Tennessee. (digital.library.unt.edu/ark:/67531/metadc1057797/: accessed September 25, 2018), University of North Texas Libraries, Digital Library, digital.library.unt.edu; crediting UNT Libraries Government Documents Department.