Partial least squares, conjugate gradient and the fisher discriminant

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The theory of multivariate regression has been extensively studied and is commonly used in many diverse scientific areas. A wide variety of techniques are currently available for solving the problem of multivariate calibration. The volume of literature on this subject is so extensive that understanding which technique to apply can often be very confusing. A common class of techniques for solving linear systems, and consequently applications of linear systems to multivariate analysis, are iterative methods. While common linear system solvers typically involve the factorization of the coefficient matrix A in solving the system Ax = b, this method can be ... continued below

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19 p.

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Faber, V. December 1996.

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This report is part of the collection entitled: Office of Scientific & Technical Information Technical Reports and was provided by UNT Libraries Government Documents Department to Digital Library, a digital repository hosted by the UNT Libraries. It has been viewed 14 times . More information about this report can be viewed below.

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Description

The theory of multivariate regression has been extensively studied and is commonly used in many diverse scientific areas. A wide variety of techniques are currently available for solving the problem of multivariate calibration. The volume of literature on this subject is so extensive that understanding which technique to apply can often be very confusing. A common class of techniques for solving linear systems, and consequently applications of linear systems to multivariate analysis, are iterative methods. While common linear system solvers typically involve the factorization of the coefficient matrix A in solving the system Ax = b, this method can be impractical if A is large and sparse. Iterative methods such as Gauss-Seidel, SOR, Chebyshev semi-iterative, and related methods also often depend upon parameters that require calibration and which are sometimes hard to choose properly. An iterative method which surmounts many of these difficulties is the method of conjugate gradient. Algorithms of this type find solutions iteratively, by optimally calculating the next approximation from the residuals.

Physical Description

19 p.

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OSTI as DE97002799

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  • Other Information: PBD: 1996

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  • Other: DE97002799
  • Report No.: LA-UR--96-3958
  • Grant Number: W-7405-ENG-36
  • DOI: 10.2172/431144 | External Link
  • Office of Scientific & Technical Information Report Number: 431144
  • Archival Resource Key: ark:/67531/metadc687078

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Office of Scientific & Technical Information Technical Reports

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Creation Date

  • December 1996

Added to The UNT Digital Library

  • July 25, 2015, 2:20 a.m.

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  • May 20, 2016, 1:40 p.m.

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Faber, V. Partial least squares, conjugate gradient and the fisher discriminant, report, December 1996; New Mexico. (digital.library.unt.edu/ark:/67531/metadc687078/: accessed September 25, 2018), University of North Texas Libraries, Digital Library, digital.library.unt.edu; crediting UNT Libraries Government Documents Department.