New Quasi-Newton Method for Solving Systems of Nonlinear Equations

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F67985807%3A_____%2F17%3A00473663" target="_blank" >RIV/67985807:_____/17:00473663 - isvavai.cz</a>
Result on the web
<a href="http://dx.doi.org/10.21136/AM.2017.0253-16" target="_blank" >http://dx.doi.org/10.21136/AM.2017.0253-16</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.21136/AM.2017.0253-16" target="_blank" >10.21136/AM.2017.0253-16</a>

Result language
angličtina
Original language name
New Quasi-Newton Method for Solving Systems of Nonlinear Equations
Original language description
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 decompositions of nonsymmetric approximations of the Jacobian matrix, so it requires O(n^2) arithmetic operations per iteration in contrast with the Newton method, which requires O(n^3) operations per iteration. Computational experiments confirm the high efficiency of the new method.
Czech name
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Czech description
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Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
—
OECD FORD branch
10102 - Applied mathematics

Project
<a href="/en/project/GA13-06684S" target="_blank" >GA13-06684S: Iterative Methods in Computational Mathematics: Analysis, Preconditioning, and Applications</a><br>
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Publication year
2017
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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