## Newton's Method (newtons_method)

Version 6.2.0 (388 KB) by
Newton's method for finding the root of a differentiable, univariate, scalar-valued function.

Updated 17 Oct 2022

From GitHub

# `newtons_method`

Newton's method for finding the root of a differentiable, univariate, scalar-valued function.

## Syntax

`x = newtons_method(f,df,x0)`
`x = newtons_method(f,df,x0,opts)`
`[x,k] = newtons_method(__)`
`[x,k,x_all] = newtons_method(__)`

## Description

`x = newtons_method(f,df,x0)` returns the root of a function specified by the function handle `f`, where `df` is the derivative of (i.e. ) and `x0` is an initial guess of the root.

`x = newtons_method(f,df,x0,opts)` does the same as the syntax above, but allows for the specification of optional solver parameters. `opts` is a structure with the following fields:

• `k_max` → maximum number of iterations (defaults to 200)
• `return_all` → returns estimates at all iteration if set to `true` (defaults to `false`)
• `TOL` → tolerance (defaults to )

`[x,k] = newtons_method(__)` also returns the number of iterations (`k`) performed of Newton's method.

`[x,k,x_all] = newtons_method(__)` does the same as the previous syntaxes, but also returns an array (`x_all`) storing the root estimates at each iteration. This syntax requires that `opts.return_all` be set to true.

• See "EXAMPLES.mlx" or the "Examples" tab on the File Exchange page for examples.

### Cite As

Tamas Kis (2023). Newton's Method (newtons_method) (https://github.com/tamaskis/newtons_method-MATLAB/releases/tag/v6.2.0), GitHub. Retrieved .

##### MATLAB Release Compatibility
Created with R2021b
Compatible with any release
##### Platform Compatibility
Windows macOS Linux

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Version Published Release Notes
6.2.0

See release notes for this release on GitHub: https://github.com/tamaskis/newtons_method-MATLAB/releases/tag/v6.2.0

6.1.0

See release notes for this release on GitHub: https://github.com/tamaskis/newtons_method-MATLAB/releases/tag/v6.1.0

6.0.2

See release notes for this release on GitHub: https://github.com/tamaskis/newtons_method-MATLAB/releases/tag/v6.0.2

6.0.0

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5.5.0

See release notes for this release on GitHub: https://github.com/tamaskis/newtons_method-MATLAB/releases/tag/v5.5.0

5.4.1

See release notes for this release on GitHub: https://github.com/tamaskis/newtons_method-MATLAB/releases/tag/v5.4.1

5.4.0

See release notes for this release on GitHub: https://github.com/tamaskis/newtons_method-MATLAB/releases/tag/v5.4.0

5.3.0

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5.2.0

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5.1.1

See release notes for this release on GitHub: https://github.com/tamaskis/newtons_method-MATLAB/releases/tag/v5.1.1

5.0.2

See release notes for this release on GitHub: https://github.com/tamaskis/newtons_method-MATLAB/releases/tag/v5.0.2

4.0.1

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4.0.0

See release notes for this release on GitHub: https://github.com/tamaskis/newtons_method-MATLAB/releases/tag/v4.0.0

3.0.5

See release notes for this release on GitHub: https://github.com/tamaskis/newtons_method-MATLAB/releases/tag/v3.0.5

3.0.3

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3.0.2

See release notes for this release on GitHub: https://github.com/tamaskis/newtons_method-MATLAB/releases/tag/v3.0.2

3.0.1

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3.0.0

See release notes for this release on GitHub: https://github.com/tamaskis/newtons_method-MATLAB/releases/tag/v3.0.0

2.0.2

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2.0.1

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2.0.0

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1.1.2

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1.1.1

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1.1.0

See release notes for this release on GitHub: https://github.com/tamaskis/newtons_method-MATLAB/releases/tag/v1.1.0

1.0.7

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1.0.6

See release notes for this release on GitHub: https://github.com/tamaskis/newtons_method-MATLAB/releases/tag/v1.0.6

1.0.5

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1.0.4

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1.0.3

See release notes for this release on GitHub: https://github.com/tamaskis/newtons_method-MATLAB/releases/tag/v1.0.3

1.0.2

See release notes for this release on GitHub: https://github.com/tamaskis/newtons_method-MATLAB/releases/tag/v1.0.2

1.0.1

See release notes for this release on GitHub: https://github.com/tamaskis/newtons_method-MATLAB/releases/tag/v1.0.1

1.0.0.0

To view or report issues in this GitHub add-on, visit the GitHub Repository.
To view or report issues in this GitHub add-on, visit the GitHub Repository.