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The evaluation of linear forms

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Abstract

This presentation deals with the evaluation and transformation of linear forms. Especial emphasis is given to implicit methods in which it is not necessary to find the explicit values,x i . The relation of the Aitken triple product matrixCA −1 B to the result of a linear transformation of linear forms is noted, and the numerical computation of this triple product matrix is indicated with the use of the simple Abbreviated Doolittle solution. Application is also made to the evaluation ofA −1 and ofA −1 C.

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References

  1. Dwyer, P. S. The solution of simultaneous equations.Psychometrika, 1941,6, 101–129.

    Google Scholar 

  2. Dwyer, P. S. The evaluation of determinants.Psychometrika, 1941,6, 191–204.

    Google Scholar 

  3. Thompson, G. H. Some points of mathematical techniques in the factorial analysis of ability.J. educ. Psychol., 1936,27, 37–54.

    Google Scholar 

  4. Aitken, A. C. Studies in practical mathematics I.Proc. Roy. Soc. of Edinburgh, 1936–37,57, 172–181. (References to earlier Aitken methods.)

    Google Scholar 

  5. Horst, Paul. A general method for evaluating multiple regression constants.J. Amer. Stat. Assoc., 1932,27, 270–278.

    Google Scholar 

  6. Waugh, F. V. A simplified method of determining multiple regression constants.J. Amer. Stat. Assoc., 1935,30, 694–700.

    Google Scholar 

  7. Dunlap, J. W. Workbook in statistical method. New York: Prentice Hall, Inc., 1939. (See especially pp. 119–120.)

    Google Scholar 

  8. Tucker, L. R. A method for finding the inverse of a matrix.Psychometrika, 1938,3, 189–197.

    Google Scholar 

  9. Hoel, P. G. On methods of solving normal equations.Annals math. Stat., 1941,12, 354–359.

    Google Scholar 

  10. Ledermann, Walter. On a shortened method of estimation of mental factors by regression.Psychometrika, 1939,4, 109–116.

    Google Scholar 

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Dwyer, P.S. The evaluation of linear forms. Psychometrika 6, 355–365 (1941). https://doi.org/10.1007/BF02288592

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