The Regula Falsi Method
Background. The Regula Falsi
method is one of the bracketing methods for finding roots of
Implementation. Given a function f(x) and an interval which might contain a root, perform a predetermined number of iterations using the Regula Falsi method.
Limitations. Investigate the result of applying the Regula Falsi method over an interval where there is a discontinuity. Apply the Regula Falsi method for a function using an interval where there are distinct roots. Apply the Regula Falsi method over a "large" interval.
Theorem (Regula Falsi
Theorem). Assume that
and that there exists a number
such that .
If have opposite signs, and
represents the sequence of points generated by the Regula Falsi process, then the sequence converges to the zero .
That is, .
Proof False Position or Regula Falsi Method False Position or Regula Falsi Method
Computer Programs False Position or Regula Falsi Method False Position or Regula Falsi Method
Mathematica Subroutine (Regula Falsi Method).
1. Find all the real solutions to the
cubic equation .
Remember. The Regula Falsi method can only be used to find a real root in an interval [a,b] in which f[x] changes sign.
2. Use the cubic
Example 1 and perform the following call to the Regula Falsi
Reduce the volume of
After you have debugged you program and it is working properly, delete the unnecessary print statements.
Concise Program for the Regula Falsi
Now test the example to see if it still works. Use the last case in Example 1 given above and compare with the previous results.
Reducing the Computational Load for the Regula Falsi Method
The following program uses fewer computations in the Regula Falsi method and is the traditional way to do it. Can you determine how many fewer functional evaluations are used ?
Various Scenarios and Animations for Regula Falsi Method.
3. Convergence Find
the solution to the cubic equation . Use
the starting interval .
Animations (Regula Falsi Method Regula Falsi Method). Internet hyperlinks to animations.
Research Experience for Undergraduates
Regula Falsi Method Regula Falsi Method Internet hyperlinks to web sites and a bibliography of articles.
Download this Mathematica Notebook Regula Falsi Method
Return to Numerical Methods - Numerical Analysis
(c) John H. Mathews 2004