ZeroFunction Class

The ZeroFunction class uses Muller's method to find the zeros of a univariate function, f(x).

For a list of all members of this type, see ZeroFunction Members.

System.Object
Imsl.Math.ZeroFunction

public class ZeroFunction

Thread Safety

Public static (Shared in Visual Basic) members of this type are safe for multithreaded operations. Instance members are not guaranteed to be thread-safe.

Remarks

ZeroFunction computes n real zeros of a real function f. Given a user-supplied function f(x) and an n-vector of initial guesses $x_1, x_2, \ldots, x_n$ , the routine uses Muller's method to locate n real zeros of f, that is, n real values of x for which f(x) = 0. The routine has two convergence criteria.

The first requires the absolute value of the function be less than the AbsoluteError. The second requires that the relative change of any two successive approximations to an be less than RelativeError. Here, is the m-th approximation to . Let AbsoluteError be $\varepsilon _1$ , and RelativeError be $\varepsilon _2$ . The criteria may be stated mathematically as follows:

Criterion 1:

$\left| {f\,\left( {x_i^m } \right)} \right| \lt \,\,\varepsilon _1$

Criterion 2:

$\left| {\frac{{x_i^{m + 1} - x_i^m }}{{x_i^m }}} \right|\; \lt \;\varepsilon _2$

"Convergence" is the satisfaction of either criterion.

Requirements

Namespace: Imsl.Math

Assembly: ImslCS (in ImslCS.dll)

ZeroFunction Class

Thread Safety

Remarks

Requirements

See Also