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Apr 7, 2025
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Add documentation for Muller's method #573

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1 change: 1 addition & 0 deletions docs/src/native/bracketingnonlinearsolve.md
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Expand Up @@ -18,4 +18,5 @@ Bisection
Falsi
Ridder
Brent
Muller
```
5 changes: 3 additions & 2 deletions docs/src/solvers/bracketing_solvers.md
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Expand Up @@ -26,13 +26,14 @@ This gives a robust and fast method, which therefore enjoys considerable popular

## Full List of Methods

### SimpleNonlinearSolve.jl
### BracketingNonlinearSolve.jl

These methods are automatically included as part of NonlinearSolve.jl. Though, one can use
SimpleNonlinearSolve.jl directly to decrease the dependencies and improve load time.
BracketingNonlinearSolve.jl directly to decrease the dependencies and improve load time.

- [`ITP`](@ref): A non-allocating ITP (Interpolate, Truncate & Project) method
- [`Falsi`](@ref): A non-allocating regula falsi method
- [`Bisection`](@ref): A common bisection method
- [`Ridder`](@ref): A non-allocating Ridder method
- [`Brent`](@ref): A non-allocating Brent method
- [`Muller`](@ref): A non-allocating Muller's method
18 changes: 14 additions & 4 deletions lib/BracketingNonlinearSolve/src/muller.jl
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"""
Muller(; middle = nothing)

Muller's method for determining a root of a univariate, scalar function. The
algorithm, described in Sec. 9.5.2 of
[Press et al. (2007)](https://numerical.recipes/book.html), requires three
initial guesses `(left, middle, right)` for the root.
Muller's method for determining a root of a univariate, scalar function.

The algorithm, described in Sec. 9.5.2 of
[Press et al. (2007)](https://numerical.recipes/book.html), is a generalization
of the secant method, using quadratic interpolation of three points to find the
next estimate for the root. Due to the quadratic interpolation, the method is
well suited for obtaining complex roots.

This method requires three initial guesses `(left, middle, right)` for the
solution. The guesses `(left, right) = tspan` are provided by the
`IntervalNonlinearProblem`, while the `middle` guess may be specified as an
optional keyword argument. In notable contrast to the other
`BracketingNonlinearSolve.jl` solvers, the `Muller` algorithm does not need
`(left, right)` to bracket the root.

### Keyword Arguments

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