Extension of Murakami's high-order non-linear solver to multiple roots
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Publication:3568440
DOI10.1080/00207160802272263zbMath1192.65052OpenAlexW1976489082MaRDI QIDQ3568440
Publication date: 11 June 2010
Published in: International Journal of Computer Mathematics (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1080/00207160802272263
Numerical computation of solutions to single equations (65H05) Complexity and performance of numerical algorithms (65Y20)
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Uses Software
Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- A family of root finding methods
- On Newton-type methods with cubic convergence
- An improvement to Ostrowski root-finding method
- Convergence of the Newton process to multiple solutions
- A composite third order Newton-Steffensen method for solving nonlinear equations
- Fourth-order derivative-free methods for solving non-linear equations
- A new family of higher order methods for solving equations
- A family of multiopoint iterative functions for finding multiple roots of equations
- A higher order method for multiple zeros of nonlinear functions
- A Family of Fourth Order Methods for Nonlinear Equations
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