Function Repository Resource:

# NumericalMethodFindRoot

Find the root of an equation or number using a specified numerical method

Contributed by: Jason Martinez
 ResourceFunction["NumericalMethodFindRoot"][f,x,method] searches for a numerical root of f as a function of x, using the specified method. ResourceFunction["NumericalMethodFindRoot"][f,{x,x0}, method] searches for a numerical root of f, starting from the point x=x0. ResourceFunction["NumericalMethodFindRoot"][f,{x,x0},method,property] returns the specified property for the numerical search.

## Details and Options

ResourceFunction["NumericalMethodFindRoot"] supports "Bisection", "Newton" and "Secant" methods.
ResourceFunction["NumericalMethodFindRoot"] has attribute HoldAll.
By default, ResourceFunction["NumericalMethodFindRoot"] returns a list of replacements for x.
ResourceFunction["NumericalMethodFindRoot"] uses the same options as FindRoot, though these are disregarded by the "Bisection" method, which overrides settings for Method.
ResourceFunction["NumericalMethodFindRoot"] supports two values for the property directive:
 "Solution" return the root of f "Steps" return a table of steps taken to reach the root
"PropertyAssociation" can be used as a fourth argument to return an Association of the properties.

## Examples

### Basic Examples (3)

Find the root of using Newton’s method:

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Specify a starting point:

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Examine step information:

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The raw data comprising the grid can be returned by applying Normal:

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### Scope (2)

Find a root using the secant method:

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Determine the steps to locating the root:

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Use complex starting points:

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### Options (1)

Get higher precision results by increasing WorkingPrecision:

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## Version History

• 1.0.0 – 11 November 2019