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Mathematics of Computation

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Analysis of third-order methods for secular equations

Author: A. Melman
Journal: Math. Comp. 67 (1998), 271-286
MathSciNet review: 1432130
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Abstract: 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

Keywords: Secular equation, nonlinear approximation, third-order convergence
Received by editor(s): May 15, 1996
Received by editor(s) in revised form: September 16, 1996
Article copyright: © Copyright 1998 American Mathematical Society