A relation between Newton and Gauss-Newton steps for singular nonlinear equations (Q1090072)
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scientific article; zbMATH DE number 4007590
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | A relation between Newton and Gauss-Newton steps for singular nonlinear equations |
scientific article; zbMATH DE number 4007590 |
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A relation between Newton and Gauss-Newton steps for singular nonlinear equations (English)
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1988
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The Gauss-Newton step belonging to an appropriately chosen bordered nonlinear system is analyzed. It is proved that the Gauss-Newton step calculated after a sequence of Newton steps is equal to the doubled Newton step within the accuracy of \(O(\| x-x^ *\| ^ 2)\). The theoretical insight given by the proof can be exploited to derive a Gauss-Newton-like algorithm for the solution of singular equations.
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bordered nonlinear system
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doubled Newton step
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singular equations
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Gauss-Newton method
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