Geometrically constructed families of Newton's method for unconstrained optimization and nonlinear equations (Q638098)
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scientific article; zbMATH DE number 5946491
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Geometrically constructed families of Newton's method for unconstrained optimization and nonlinear equations |
scientific article; zbMATH DE number 5946491 |
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Geometrically constructed families of Newton's method for unconstrained optimization and nonlinear equations (English)
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9 September 2011
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Summary: One-parameter families of Newton's iterative method for the solution of nonlinear equations and its extension to unconstrained optimization problems are presented in the paper. These methods are derived by implementing approximations through a straight line and through a parabolic curve in the vicinity of the root. The presented variants are found to yield better performance than Newton's method, in addition that they overcome its limitations.
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