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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.

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Analysis of third-order methods for secular equations
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by A. Melman PDF
Math. Comp. 67 (1998), 271-286 Request permission


Third-order numerical methods are analyzed for secular equations. These equations arise in several matrix problems and numerical linear algebra applications. A closer look at an existing method shows that it can be considered as a classical method for an equivalent problem. This not only leads to other third-order methods, it also provides the means for a unifying convergence analysis of these methods and for their comparisons. Finally, we consider approximated versions of the aforementioned methods.
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Additional Information
  • A. Melman
  • Affiliation: Department of Industrial Engineering, Ben-Gurion University, Beer-Sheva 84105, Israel
  • MR Author ID: 293268
  • Email:
  • Received by editor(s): May 15, 1996
  • Received by editor(s) in revised form: September 16, 1996
  • © Copyright 1998 American Mathematical Society
  • Journal: Math. Comp. 67 (1998), 271-286
  • DOI:
  • MathSciNet review: 1432130