Sidi's generalized secant method

<p>Sidi's generalized secant method is a <a href="/facts/Root-finding_algorithm/IxTDkhBq">root-finding algorithm</a>, that is, a <a href="/facts/Numerical_method/MrQIMSIY">numerical method</a> for solving <a href="/facts/Equations/pxFzLAVR">equations</a> of the form 
  
    
      
        f
        (
        x
        )
        =
        0
      
    
    {\displaystyle f(x)=0}
  
 . The method was published
by Avram Sidi.
</p><p>The method is a generalization of the <a href="/facts/Secant_method/tkNV8Rzk">secant method</a>. Like the secant method, it is an <a href="/facts/Iterative_method/uKMAJhEh">iterative method</a> which requires one evaluation of 
  
    
      
        f
      
    
    {\displaystyle f}
  
 in each iteration and no <a href="/facts/Derivative/7Ito70Dh">derivatives</a> of 
  
    
      
        f
      
    
    {\displaystyle f}
  
. The method can converge much faster though, with an <a href="/facts/Rate_of_convergence/JVGuzPoS">order</a> which approaches 2 provided that 
  
    
      
        f
      
    
    {\displaystyle f}
  
 satisfies the regularity conditions described below.
</p>

Sidi's generalized secant method open-in-new

Sidi's generalized secant method