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Shinozaki, Nobuo; Sibuya, Masaaki; Tanabe, Kunio

Numerical algorithms for the Moore-Penrose inverse of a matrix: iterative methods. (English) Zbl 0314.65016

Ann. Inst. Stat. Math. 24, 621-629 (1972).
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Cited in 4 Documents

MSC:

65F20 Numerical solutions to overdetermined systems, pseudoinverses
65F10 Iterative numerical methods for linear systems
15A09 Theory of matrix inversion and generalized inverses
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References:

[1] Ben-Israel, A and Cohen, D. (1966). On iterative computation of generalized inverses and associated projections,SIAM Jour. Numer. Anal.,3, 410–419. · Zbl 0143.37402 · doi:10.1137/0703035
[2] Boullion, T. L. and Odell, P. L. (1971).Generalized Inverse Matrices, Wiley-Interscience, New York. · Zbl 0223.15002
[3] Garnett, J. M., III, Ben-Israel, A. and Yau, S. S. (1971). A hyperpower iterative method for computing matrix products involving the generalized inverse,SIAM Jour. Numer. Anal.,8, 104–109. · Zbl 0217.52605 · doi:10.1137/0708013
[4] Petryshyn, W. V. (1967). On generalized inverses and on the uniform convergence of (1K) n with application to, iterative methods,Jour. Math. Anal. Appl.,18, 417–439. · Zbl 0189.47502 · doi:10.1016/0022-247X(67)90036-4
[5] Pringle, R. M. and Rayner, A. A. (1972).Generalized Inverse Matrices with Applications to Statistics, Charles Griffin, London. · Zbl 0231.15008
[6] Rao, C. R. and Mitra, S. K. (1971)Generalized Inverse Matrices and Its Applications, Wiley, New York. · Zbl 0236.15004
[7] Shinozaki, N., Sibuya, M. and Tanabe, K. (1972). Numerical algorithms for the Moore-Penrose inverse of a matrix: Direct methods,Ann. Inst. Statist. Math.,24, 193–203. · Zbl 0315.65027 · doi:10.1007/BF02479751
[8] Tanabe, K. (1971). An adaptive acceleration of general linear iterative processes for solving systems of linear equations,Res. Memo. Inst. Statist. Math., No. 43. · Zbl 0228.65032
[9] Zlobec, S. (1967). On computing the generalized inverse of a linear operator,Glasnik Matematicki,2(22), 265–271. · Zbl 0149.35101
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