Function Repository Resource:

NewtonsMethodFindRoot

Determine the root of an equation using Newton's method

Contributed by: Jason Martinez

ResourceFunction["NewtonsMethodFindRoot"][f,{x,x₀},tol]

searches for a numerical root of f starting at x₀ with digits equal to tol.

ResourceFunction["NewtonsMethodFindRoot"][lhs⩵rhs,{x,x₀},tol]

searches for a numerical solution to the equation lhs==rhs.

ResourceFunction["NewtonsMethodFindRoot"][f,{x,x₀},tol,property]

returns a property of the search for the root of f.

Details

ResourceFunction["NewtonsMethodFindRoot"] supports two options for property:

"Solution"

return root of f

"Steps"

return a table of steps taken to reach the root

"PropertyAssociation" can be used to return an Association of the properties.

Find the root of an expression using Newton’s method:

In[1]:=

Out[1]=

Determine the steps to find the root of an equation:

In[2]:=

Out[2]=

Get the property Association of Newton's method:

In[3]:=

$ResourceFunction["NewtonsMethodFindRoot"][ x^2 - 2 x, {x, 5}, 5, "PropertyAssociation"]$

Out[3]=