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Merge pull request #25 from rickecon/typo
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rickecon authored Dec 6, 2023
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Expand Up @@ -100,7 +100,7 @@ Many systems of equations that occur in theoretical models are *exactly identifi

It is *not* widely recognized among researchers that even in systems of equations for which existence and uniqueness of the solution can be proven, no root finding algorithm with finite computational power exists that guarantees convergence to the solution of the system in every case. Judd states:

> Nonlinear equation solving presents problems not present with linear equations or optimization. In particular, the existence problem is much more difficult for nonlinear systems. Unless one has an existence proof in had, a programmer must keep in mind that the absence of a solutino may explain a program's failure to converge. Ever if there exists a solution, all methods will do poorly if the problem is poorly conditioned near a solution. Transforming the problem will often improve performance.{cite}`Judd:1998` (p. 192)
> Nonlinear equation solving presents problems not present with linear equations or optimization. In particular, the existence problem is much more difficult for nonlinear systems. Unless one has an existence proof in hand, a programmer must keep in mind that the absence of a solution may explain a program's failure to converge. Even if there exists a solution, all methods will do poorly if the problem is poorly conditioned near a solution. Transforming the problem will often improve performance.{cite}`Judd:1998` (p. 192)
Because root finding in nonlinear systems can be so difficult, much research into the best methods has accumulated over the years. And the approaches to solving nonlinear systems can be an art as much as a science. This is also true of minimization problems discussed in the next section ({ref}`SecSciPyMin`). For this reason, the [`scipy.optimize.root`](https://docs.scipy.org/doc/scipy/reference/generated/scipy.optimize.root.html) module has many different solution algorithms you can use to find the solution to a nonlinear system of equations (e.g., `hybr`, `lm`, `linearmixing`).

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