A COMPARISON OF SEVERAL METHODS FOR INVERTING LARGE SYMMETRIC POSITIVE DEFINITE MATRICES

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ABS>The Gauss-Jordan, Choleski, congruent transformation, and rank annihilation methods for inverting large symmetric positive definite matrices were compared. An attempt was made to consider the effects of both condition and order of the matrix to be inverted on the closeness of the computed inverse to the exact inverse. Each method was programmed in FORTRAN using only single precision arithmetic. Then the error indicators were computed using double precision arithmetic so that the latter calculation was not a limiting factor. It was found that any one of the methods is satisfactory for a well-conditioned least squares matrix of order 10-30. However, ... continued below

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Pages: 34

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Lietzke, M.H.; Stoughton, R.W. & Lietzke, M.P. May 13, 1963.

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ABS>The Gauss-Jordan, Choleski, congruent transformation, and rank annihilation methods for inverting large symmetric positive definite matrices were compared. An attempt was made to consider the effects of both condition and order of the matrix to be inverted on the closeness of the computed inverse to the exact inverse. Each method was programmed in FORTRAN using only single precision arithmetic. Then the error indicators were computed using double precision arithmetic so that the latter calculation was not a limiting factor. It was found that any one of the methods is satisfactory for a well-conditioned least squares matrix of order 10-30. However, when the matrix becomes ill- conditioned then the Gauss-Jordan method appears to be clearly superior (at least for the matrices studied). Algorithms and FORTRAN subroutines for each method are presented. (auth)

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Pages: 34

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  • Other Information: Orig. Receipt Date: 31-DEC-63

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  • Report No.: ORNL-3430
  • Grant Number: W-7405-ENG-26
  • DOI: 10.2172/4721949 | External Link
  • Office of Scientific & Technical Information Report Number: 4721949
  • Archival Resource Key: ark:/67531/metadc1034537

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  • May 13, 1963

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  • Oct. 18, 2017, 7:39 a.m.

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  • Oct. 23, 2017, 12:23 p.m.

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Lietzke, M.H.; Stoughton, R.W. & Lietzke, M.P. A COMPARISON OF SEVERAL METHODS FOR INVERTING LARGE SYMMETRIC POSITIVE DEFINITE MATRICES, report, May 13, 1963; Oak Ridge, Tennessee. (digital.library.unt.edu/ark:/67531/metadc1034537/: accessed December 11, 2017), University of North Texas Libraries, Digital Library, digital.library.unt.edu; crediting UNT Libraries Government Documents Department.