NAG Library Function Document

nag_zero_cont_func_cntin (c05awc)

1  Purpose

2  Specification

3  Description

4  References

5  Arguments

1:     x – double *Input/Output

On entry: an initial approximation to the zero.

On exit: if $\mathbf{fail}\mathbf{.}\mathbf{code}=$ NE_NOERROR, NE_SECANT_ITER_FAILED or NE_TOO_MANY_CALLS it contains the approximation to the zero, otherwise it contains no useful information.

2:     eps – doubleInput

On 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 $\alpha$. Indeed, for very small positive values of eps, it is likely that the final approximation will satisfy $\left|\mathbf{x}-\alpha \right|<\mathbf{eps}$. You are advised to call the function with more than one value for eps to check the accuracy obtained.

Constraint: $\mathbf{eps}>0.0$.

3:     eta – doubleInput

On entry: a value such that if $\left|f\left(x\right)\right|<\mathbf{eta}$, $x$ is accepted as the zero. eta may be specified as $0.0$ (see Section 7).

4:     f – function, supplied by the userExternal Function

f must evaluate the function $f$ whose zero is to be determined.

The specification of f is:

double  f (double x, Nag_Comm *comm)

1:     x – doubleInput

On entry: the point at which the function must be evaluated.

2:     comm – Nag_Comm *

Pointer to structure of type Nag_Comm; the following members are relevant to f.

user – double *

iuser – Integer *

p – Pointer 

The type Pointer will be void *. Before calling nag_zero_cont_func_cntin (c05awc) you may allocate memory and initialize these pointers with various quantities for use by f when called from nag_zero_cont_func_cntin (c05awc) (see Section 3.2.1.1 in the Essential Introduction).

5:     nfmax – IntegerInput

On entry: the maximum permitted number of calls to f from nag_zero_cont_func_cntin (c05awc). If f is inexpensive to evaluate, nfmax should be given a large value (say $>1000$).

Constraint: $\mathbf{nfmax}>0$.

6:     comm – Nag_Comm *Communication Structure

The NAG communication argument (see Section 3.2.1.1 in the Essential Introduction).

7:     fail – NagError *Input/Output

The NAG error argument (see Section 3.6 in the Essential Introduction).

6  Error Indicators and Warnings

NE_BAD_PARAM

On entry, argument $⟨\mathit{\text{value}}⟩$ had an illegal value.

NE_INT

On entry, $\mathbf{nfmax}=⟨\mathit{\text{value}}⟩$.
Constraint: $\mathbf{nfmax}>0$.

NE_INTERNAL_ERROR

An internal error has occurred in this function. Check the function call and any array sizes. If the call is correct then please contact NAG for assistance.

A serious error occurred in an internal call to an auxiliary function.

Internal scale factor invalid for this problem. Consider using nag_zero_cont_func_cntin_rcomm (c05axc) instead and setting scal.

NE_REAL

On entry, $\mathbf{eps}=⟨\mathit{\text{value}}⟩$.
Constraint: $\mathbf{eps}>0.0$.

NE_SECANT_ITER_FAILED

Either f has no zero near x or too much accuracy has been requested. Check the coding of f or increase eps.

NE_TOO_MANY_CALLS

More than nfmax calls have been made to f.

nfmax may be too small for the problem (because x is too far away from the zero), or f has no zero near x, or too much accuracy has been requested in calculating the zero. Increase nfmax, check the coding of f or increase eps.

7  Accuracy

8  Parallelism and Performance

9  Further Comments

10  Example

10.1  Program Text

Program Text (c05awce.c)

10.2  Program Data

10.3  Program Results

Program Results (c05awce.r)