Iterative Methods for the Solutions of Equations

Traub, Joseph F.

doi:10.2307/2004117

Cited by 232 publications

(458 citation statements)

References 0 publications

Supporting

Mentioning

428

Contrasting

Unclassified

Order By: Relevance

“…The proofs are rather technical and we shall not consider them here. They are similar to results of the same type in [23].…”

Section: Second Derivative Approximationssupporting

confidence: 91%

“…The convergence of Newton's method is immediate in this case (see, e.g., [15,19,23] also converge and their cubic order of convergence folllows from, e.g., [23]. We also note that the inequalities imply that, for our problem, the step in Euler's method is larger than for Halley's.…”

Section: Convergencementioning

confidence: 61%

“…When G (γ) = 0, the approximation degenerates into a line. In fact, the standard way the approximation is presented (see [20,21,23]) is…”

Section: Transformation Of Variables and Halley's Methodsmentioning

confidence: 99%

“…The convergence is then immediate from a classical result for Newton's method (see, e.g., [15,19,23]). …”

Section: Theorem 42 Euler's and Halley's Methods Converge From Any mentioning

confidence: 99%

“…(see [23]). The special form of our problem, obtained by transforming both the variable, t = 1/γ, License or copyright restrictions may apply to redistribution; see http://www.ams.org/journal-terms-of-use and the function, φ(γ) = (γ − 1/δ)F (γ), makes the convergence analysis of such methods relatively easy.…”

Section: Second Derivative Approximationsmentioning

confidence: 99%

See 4 more Smart Citations

Analysis of third-order methods for secular equations

Melman

1998

Math. Comp.

View full text Add to dashboard Cite

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.

show abstract

“…The proofs are rather technical and we shall not consider them here. They are similar to results of the same type in [23].…”

Section: Second Derivative Approximationssupporting

confidence: 91%

Section: Convergencementioning

confidence: 61%

“…When G (γ) = 0, the approximation degenerates into a line. In fact, the standard way the approximation is presented (see [20,21,23]) is…”

Section: Transformation Of Variables and Halley's Methodsmentioning

confidence: 99%

“…The convergence is then immediate from a classical result for Newton's method (see, e.g., [15,19,23]). …”

Section: Theorem 42 Euler's and Halley's Methods Converge From Any mentioning

confidence: 99%