Householder A.S. (1955), Terminating and non-terminating iterations for solving linear systems, J. SIAM, 3, 67-72.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....null space methods will also see a connection. To give an idea of the frequency with which these ideas have been discovered and rediscovered, some the earlier papers are itemized in the following table Fox, Huskey and Wilkinson [9] 1948 Hestenes and Stiefel [12] 1952 Purcell [16] 1953 Householder [13] 1955 Pietrzykowski [15] 1960 Faddeev and Faddeeva [7] 1963 Stewart [19] 1973 Enderson and Wassyng [6] 1978 Sloboda [18] 1978 Wassyng [23] 1982 Abaffy, Broyden and Spedicato [1] 1984 Hegedus [11] 1986 Most of the papers develop the method as an iterative method based on conjugacy and orthogonality ....

Householder A.S. (1955), Terminating and non-terminating iterations for solving linear systems, J. SIAM, 3, 67-72.

....computational point of view. Perhaps the earliest reference to a variant of DPM for general matrices can be found in Hestenes and Stiefel [11] in their landmark paper on the conjugate gradient method (see pp. 426 427) Other contributions are due to Purcell [15] Pietrzykowski [14] Householder [12], 13] Faddeev and Faddeeva [9] Stewart [17] Sloboda [16] and Aba#y, Broyden, and Spedicato [1] For symmetric positive definite matrices, the algorithm essentially becomes a conjugate direction method already considered by Fox, Huskey, and Wilkinson [10] and by Hestenes and Stiefel [11] ....

A. S. Householder, Terminating and nonterminating iterations for solving linear systems, J. Soc. Indust. Appl. Math., 3 (1955), pp. 67--72.

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