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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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A unifying convergence analysis of second-order methods for secular equations
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by A. Melman PDF
Math. Comp. 66 (1997), 333-344 Request permission


Existing numerical methods of second-order are considered for a so-called secular equation. We give a brief description of the most important of these methods and show that all of them can be interpreted as improvements of Newton’s method for an equivalent problem for which Newton’s method exhibits convergence from any point in a given interval. This interpretation unifies the convergence analysis of these methods, provides convergence proofs where they were lacking and furnishes ways to construct improved methods. In addition, we show that some of these methods are, in fact, equivalent. A second secular equation is also briefly considered.
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Additional Information
  • A. Melman
  • Affiliation: Department of Industrial Engineering and Management, Ben-Gurion University, Beer-Sheva 84105, Israel
  • MR Author ID: 293268
  • Email:
  • Received by editor(s): February 12, 1995
  • Received by editor(s) in revised form: November 13, 1995
  • © Copyright 1997 American Mathematical Society
  • Journal: Math. Comp. 66 (1997), 333-344
  • MSC (1991): Primary 65F15, 65H05
  • DOI:
  • MathSciNet review: 1370854