Algorithms regula falsi

In this and the next subsection, we outline algorithms for finding roots of single-variable equations of the form f(x) = 0. The first procedure, termed the regula-falsi method, is appropriately used when an analytical expression for the derivative of / with respect to x is not available—as. for example, when f x) is obtained as the output of a computer program for an input value of x. The algorithm is as follows ... 

The regula-falsi method is the procedure used by many spreadsheet programs in their goalseek algorithms. 

The two points retained for the next step are x and either Xq or x, the choice being made so that the pair of values/(Jc), and either/(jc ) or/(jc ), have opposite signs to maintain the bracket on x. (This variation is called regula falsi or the method of felse position.) In Figure L.7, for the k + l)st stage, x and Xq would be selected as the end points of the secant line. Secant methods may seem crude, but they work well in practice. The details of the computational aspects of a sound algorithm to solve multiple equations by the secant method are too lengthy to outline here (particularly the calculation of a new Jacobian matrix from the former one instead refer to Dennis and Schnabel"). 

The regula falsi algorithm is very similar to the previous one. The difference is in the support points adopted to linearize the function the last two values at each iteration are used in the secant method, whereas the boundaries of the interval of uncertainty are adopted in the regula falsi method. 

The zero root of the function can be found by an application of the Regula Falsi, taking care of the possible range of values. The algorithm [6] is defined by... 

Figure 2.13 MATLAB file regfals.m that implements the Regula Falsi algorithm.

REGFALS Find a zero of a nonlinear equation of one variable /, using the regula falsi algorithm. Func is the name of... 

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