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Mathematics of Computation

Published by the American Mathematical Society, the Mathematics of Computation (MCOM) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6842 (online) ISSN 0025-5718 (print)

The 2020 MCQ for Mathematics of Computation is 1.98.

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Methods for modifying matrix factorizations
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by P. E. Gill, G. H. Golub, W. Murray and M. A. Saunders PDF
Math. Comp. 28 (1974), 505-535 Request permission


In recent years, several algorithms have appeared for modifying the factors of a matrix following a rank-one change. These methods have always been given in the context of specific applications and this has probably inhibited their use over a wider field. In this report, several methods are described for modifying Cholesky factors. Some of these have been published previously while others appear for the first time. In addition, a new algorithm is presented for modifying the complete orthogonal factorization of a general matrix, from which the conventional QR factors are obtained as a special case. A uniform notation has been used and emphasis has been placed on illustrating the similarity between different methods.
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  • J. H. Wilkinson, The algebraic eigenvalue problem, Clarendon Press, Oxford, 1965. MR 0184422
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Additional Information
  • © Copyright 1974 American Mathematical Society
  • Journal: Math. Comp. 28 (1974), 505-535
  • MSC: Primary 65F05
  • DOI:
  • MathSciNet review: 0343558