Estimation with singular inverses

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Bjerhammar, Arne (2011)

The classical estimation procedure according to Gauss uses the inversion of non-singular matrices. The author has earlier presented a number of papers concerning the stochastical estimation with the use of singular inverses (Bjerhammar, 1948–1958). The present paper gives a review of the earlier contributions and an application to selected problems. For a geodetic network all points can be considered unknown and an estimate with a generalized inverse gives the minimum variance of the observations as well as the unknowns. This estimate is invariant with respect to rotations and translations, and therefore of special interest for the study of the optimum network. It is furthermore of interest because it eliminates the dependence on the coordinate system. A number of similar applications can be found in most sciences.DOI: 10.1111/j.2153-3490.1971.tb00603.x
  • References (18)
    18 references, page 1 of 2

    Boarda, W. 1949. Some remarks on the computation and adjustment of large systems of geodetic triangulation. Report to the IoU.G.G. at Rome, Netherlands Geodetic Commission.

    Bjerhammar, A. 1948. NAgra synpunkter pA matriskalkylens anvandning inom utjimningsrakningen. [Some considerations regarding the application of the calculus of matrices to the method of least squares.] Svensk Lantmiiteritidakrift.

    Bjerhammar, A. 1949. Metoder for forenkling av utjamningsrakningen enligt minsta kvadratprincipen. [Methods for simplification of adjustment by means of the method of least squares.] Svensk LantmiiteritidBkrift.

    Bjerhammar, A. 1951. Application of calculus of matrices to method of least squares with special references to geodetic calculations. Trans. of the Royal Institute of Technology, Stockholm, no. 49.

    Bjerhammar, A. 1955. En ny matrisalgebra. Svensk LantmiiteritidBkrift, 5-6.

    Bjerhammar, A. 1958. A generalized matrix algebra. Stockholm.

    Cramer, H. 1945. Mathematical methoda of 8tati8tics. Uppsala.

    Doolittle, M. H. 1878. On least squares solutions. U.S.G.G.S., Annual Report, App. 8, Paper 3, II5-20.

    Fox. L., Huskey, H. D. & Wilkinson, J. H. 1948. Notes on the solution of algebraic linear simulta· neous equations. Mech. App. Matka. 1, 149-73.

    Greville, T. N. E. 1960. Some applications of the pseudoinverse of a matrix. SIAM Review Z, No. 1.

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