Conjugate Gradients and Related KMP Algorithms: The Beginnings
Conjugate Gradients and Related KMP Algorithms: The Beginnings
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Date
1998-10-15
Authors
O'Leary, Dianne P.
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Abstract
In the late 1940's and early 1950's, newly available computing
machines generated intense interest in solving ``large'' systems
of linear equations. Among the algorithms developed were several
related methods, all of which generated bases for Krylov subspaces
and used the bases to minimize or orthogonally project a measure
of error. These methods include the conjugate gradient algorithm
and the Lanczos algorithm. We refer to these algorithms as the
KMP family and discuss its origins, emphasizing research themes
that continue to have central importance.
(Also cross-referenced as UMIACS-TR-95-107)