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Lemeire, Frans

Equilibration of matrices to optimize backward numerical stability. (English) Zbl 0329.65029

BIT, Nord. Tidskr. Inf.-behandl. 16, 143-145 (1976).
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scan of Zbl 0329.65029

MSC:

65G50 Roundoff error
65F10 Iterative numerical methods for linear systems
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References:

[1] F. L. Bauer,Optimal scaling of matrices and the importance of minimal condition, C. M. Popplewell, North-Holland Publ. Co., Amsterdam, pp 198–201, 1962.
[2] F. L. Bauer,Optimally scaled matrices, Numer. Math., vol. 5, pp. 73–87, 1963. · Zbl 0107.10501 · doi:10.1007/BF01385880
[3] Å. Björk,Solving linear least squares problems by Gram-Schmidt orthogonalization, BIT, vol. 7, no. 1, pp. 1–21, 1967. · Zbl 0183.17802 · doi:10.1007/BF01934122
[4] F. Lemeire,Konditionering en numerieke stabiliteit in de matriksrekening, Doctoral thesis, Katholieke Universiteit Leuven, Afdeling Toegepaste Wiskunde en Programmatie, Belgium (1974).
[5] A. W. Marshall, I. Olkin,Scaling of matrices to achieve specified row and column sums, Numer. Math., vol. 12, no. 1, pp. 83–90, 1968. · Zbl 0165.17401 · doi:10.1007/BF02170999
[6] E. E. Osborne,On preconditioning of matrices, J.A.C.M., vol. 7, no. 1, pp. 338–345, 1960. · Zbl 0106.31604
[7] B. N. Parlett, C. Reinsch,Balancing a matrix for calculation of eigenvalues and eigenvectors, Numer. Math., vol. 13, no. 5, pp. 293–304, 1969. · Zbl 0184.37703 · doi:10.1007/BF02165404
[8] A. van der Sluis,Equilibration and pivoting in linear algebraic systems, Information Processing 68, pp. 127–129, North-Holland Publ. Co., Amsterdam, 1969. · Zbl 0194.46704
[9] A. van der Sluis,Condition numbers and equilibration of matrices, Numer. Math., vol. 14, no. 1, pp. 14–23, 1969. · Zbl 0182.48906 · doi:10.1007/BF02165096
[10] A. van der Sluis,Condition, equilibration and pivoting in linear algebraic systems, Numer. Math., vol. 15, pp. 74–86, 1970. · Zbl 0182.49002 · doi:10.1007/BF02165662
[11] J. H. Wilkinson,Rounding errors in algebraic processes, Her Majesty’s Stationary Office, London, 1963.
[12] J. H. Wilkinson,The algebraic eigenvalue problem, Clarendon Press, Oxford, 1965. · Zbl 0258.65037
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