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Mathematics of Computation

Published by the American Mathematical Society since 1960 (published as Mathematical Tables and other Aids to Computation 1943-1959), Mathematics of Computation is devoted to research articles of the highest quality in computational mathematics.

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

The 2020 MCQ for Mathematics of Computation is 1.78.

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.


Error analysis of some techniques for updating orthogonal decompositions
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by C. C. Paige PDF
Math. Comp. 34 (1980), 465-471 Request permission


We consider accurate and efficient methods for updating the result of the transformation $C = BQ$, Q orthogonal, of a given matrix B when Q is available. Adding or deleting a row, or adding a column of B leads to a continuation of the original transformation, and as such is numerically stable. In particular, we discuss a well-known method for updating when a column of B is deleted, and show that it is as numerically stable as the problem allows. The results extend to two-sided transformations of the form $C = {Z^T}BQ$. The methods and analyses are independent of the form or rank of B and C, and so are widely applicable.
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Additional Information
  • © Copyright 1980 American Mathematical Society
  • Journal: Math. Comp. 34 (1980), 465-471
  • MSC: Primary 65F30
  • DOI:
  • MathSciNet review: 559196