Function Repository Resource:

SecantMethodFindRoot

Determine the root of an equation using the secant method

Contributed by: Jason Martinez

ResourceFunction["SecantMethodFindRoot"][f,{x,x₀,x₁},prec]

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

ResourceFunction["SecantMethodFindRoot"][lhs⩵rhs,{x,x₀,x₁},prec]

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

ResourceFunction["SecantMethodFindRoot"][f,{x,x₀,x₁},prec,property]

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

Details

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

"Solution"

return the 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 the secant method:

In[1]:=

$ResourceFunction["SecantMethodFindRoot"][x^2 - 30, {x, 5, 6}, 10]$

Out[1]=

Determine the steps to find the root of an equation:

In[2]:=

Out[2]=

Get the property Association of the secant method:

In[3]:=

$ResourceFunction["SecantMethodFindRoot"][ x^2 - 2 x, {x, 5, 6}, 6, "PropertyAssociation"]$

Out[3]=