Abstract
The main difference with the linear case is explained. Univariate problems are used as an introduction to the more interesting multivariate case. Fixed-point iteration, Newton’s method, and quasi-Newton methods are presented, and contrasted from the point of view of their convergence speeds. Since all of them are iterative and local, the questions of where to start from and when to stop cannot be avoided. Pointers are given to guaranteed methods that look for all the solutions, thus bypassing the problem of initialization.
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Walter, É. (2014). Solving Systems of Nonlinear Equations. In: Numerical Methods and Optimization. Springer, Cham. https://doi.org/10.1007/978-3-319-07671-3_7
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DOI: https://doi.org/10.1007/978-3-319-07671-3_7
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