Abstract
A generalization of the class of direct methods for linear systems recently introduced by Abaffy, Broyden and Spedicato is obtained by applying these algorithms to a scaled system. The resulting class contains an essentially free parameter at each step, giving a unified approach to finitely terminating methods for linear systems. Various properties of the generalized class are presented. Particular attention is paid to the subclasses that contain the classic Hestenes-Stiefel method and the Hegedus-Bodocs biorthogonalization methods.
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This work was partially supported by CNR under contract 85.02648.01.
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Abaffy, J., Spedicato, E. A class of scaled direct methods for linear systems. Ann Inst Stat Math 42, 187–201 (1990). https://doi.org/10.1007/BF00050789
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DOI: https://doi.org/10.1007/BF00050789