Summary
A generalizeds-term truncated conjugate gradient method of least square type, proposed in [1a, b], is extended to a form more suitable for proving when the truncated version is identical to the full-term version. Advantages with keeping a control term in the truncated version is pointed out. A computationally efficient new algorithm, based on a special inner product with a small demand of storage is also presented.
We also give simplified and slightly extended proofs of termination of the iterative sequence and of existence of ans-term recursion, identical to the full-term version. Important earlier results on this latter topic are found in [15, 16, 8 and 11].
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The research reported in this paper was partly supported by NATO Grant No. 648/83
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Axelsson, O. A generalized conjugate gradient, least square method. Numer. Math. 51, 209–227 (1987). https://doi.org/10.1007/BF01396750
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DOI: https://doi.org/10.1007/BF01396750