c05aw attempts to locate a zero of a continuous function using a continuation method based on a secant iteration.
Public Shared Sub c05aw ( _ ByRef x As Double, _ eps As Double, _ eta As Double, _ f As C05..::..C05AW_F, _ nfmax As Integer, _ <OutAttribute> ByRef ifail As Integer _ )
public: static void c05aw( double% x, double eps, double eta, C05..::..C05AW_F^ f, int nfmax, [OutAttribute] int% ifail )
- Type: System..::..Double%On entry: an initial approximation to the zero.On exit: the final approximation to the zero, unless , or , in which case it contains no useful information.
- Type: System..::..DoubleOn entry: an absolute tolerance to control the accuracy to which the zero is determined. In general, the smaller the value of eps the more accurate x will be as an approximation to . Indeed, for very small positive values of eps, it is likely that the final approximation will satisfy . You are advised to call the method with more than one value for eps to check the accuracy obtained.Constraint: .
- Type: System..::..Double
- Type: NagLibrary..::..C05..::..C05AW_Ff must evaluate the function whose zero is to be determined.
A delegate of type C05AW_F.
- Type: System..::..Int32On entry: the maximum permitted number of calls to f from c05aw. If f is inexpensive to evaluate, nfmax should be given a large value (say ).Constraint: .
c05aw attempts to obtain an approximation to a simple zero of the function given an initial approximation to . The zero is found by a call to c05ax whose specification should be consulted for details of the method used.
The approximation to the zero is determined so that at least one of the following criteria is satisfied:
Errors or warnings detected by the method:
On entry, .
Constraint: .On entry, .
A serious error occurred in an internal call to an auxiliary method.
The levels of accuracy depend on the values of eps and eta. If full machine accuracy is required, they may be set very small, resulting in an exit with or , although this may involve many more iterations than a lesser accuracy. You are recommended to set and to use eps to control the accuracy, unless you have considerable knowledge of the size of for values of near the zero.
The time taken by c05aw depends primarily on the time spent evaluating the function (see [Parameters]) and on how close the initial value of x is to the zero.
This example calculates the zero of from a starting value . Two calculations are made with and for comparison purposes, with in both cases.