New quasi-Newton method for solving systems of nonlinear equations.
| Autor: | Lukšan, Ondřej |
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| Jazyk: | angličtina |
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články
journal articles nelineární rovnice systém rovnic metoda důvěryhodnosti kvazi-Newtonovské metody Broydenova metoda numerické algoritmy numerické experimenty nonlinear equations system of equations trust-region method quasi-Newton method adjoint Broyden method numerical algorithms numerical experiments |
| Druh dokumentu: | Non-fiction |
| ISSN: | 0862-7940 |
| Abstrakt: | Abstract: We propose a new Broyden method for solving systems of nonlinear equations, which uses the first derivatives, but is more efficient than the Newton method (measured by the computational time) for larger dense systems. The new method updates QR or LU decompositions of nonsymmetric approximations of the Jacobian matrix, so it requires O(n²) arithmetic operations per iteration in contrast with the Newton method, which requires O(n³) operations per iteration. Computational experiments confirm the high efficiency of the new method. |
| Databáze: | Katalog Knihovny AV ČR |
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