Finding roots of equations in given neighborhoods (Q1091767)
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scientific article; zbMATH DE number 4011799
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Finding roots of equations in given neighborhoods |
scientific article; zbMATH DE number 4011799 |
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Finding roots of equations in given neighborhoods (English)
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1987
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For the numerical solution of certain nonlinear systems in n variables the author considers the homotopy defined by \(H(t,x)=(f(a+t(x-a))-f(a)/t\) for \(0<t\leq 1\) and \(H(0,x)=f'(a)(x-a),\) and proves the existence of the solution trajectory on suitable sets. There is little attempt to show the connection to known results of numerical homotopy theory in the literature.
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Newton's method
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rates of convergence
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homotopy method
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existence of trajectory
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