NAG Library Function Document

nag_zero_cont_func_brent (c05ayc)

1  Purpose

2  Specification

3  Description

4  References

5  Arguments

1:     a – doubleInput

On entry: $a$, the lower bound of the interval.

2:     b – doubleInput

On entry: $b$, the upper bound of the interval.

Constraint: $\mathbf{b}\ne \mathbf{a}$.

3:     eps – doubleInput

On entry: the termination tolerance on $x$ (see Section 3).

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

4:     eta – doubleInput

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

5:     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_brent (c05ayc) you may allocate memory and initialize these pointers with various quantities for use by f when called from nag_zero_cont_func_brent (c05ayc) (see Section 3.2.1.1 in the Essential Introduction).

6:     x – double *Output

On exit: if $\mathbf{fail}\mathbf{.}\mathbf{code}=$ NE_NOERROR or NE_TOO_SMALL, x is the final approximation to the zero. If $\mathbf{fail}\mathbf{.}\mathbf{code}=$ NE_PROBABLE_POLE, x is likely to be a pole of $f\left(x\right)$. Otherwise, x contains no useful information.

7:     comm – Nag_Comm *Communication Structure

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

8:     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_FUNC_END_VAL

On entry, $\mathbf{f}\left(\mathbf{a}\right)$ and $\mathbf{f}\left(\mathbf{b}\right)$ have the same sign with neither equalling $0.0$: $\mathbf{f}\left(\mathbf{a}\right)=⟨\mathit{\text{value}}⟩$ and $\mathbf{f}\left(\mathbf{b}\right)=⟨\mathit{\text{value}}⟩$.

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.

NE_PROBABLE_POLE

The function values in the interval $\left[\mathbf{a},\mathbf{b}\right]$ might contain a pole rather than a zero. Reducing eps may help in distinguishing between a pole and a zero.

NE_REAL

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

NE_REAL_2

On entry, $\mathbf{a}=⟨\mathit{\text{value}}⟩$ and $\mathbf{b}=⟨\mathit{\text{value}}⟩$.
Constraint: $\mathbf{a}\ne \mathbf{b}$.

NE_TOO_SMALL

No further improvement in the solution is possible. eps is too small: $\mathbf{eps}=⟨\mathit{\text{value}}⟩$. The final value of x returned is an accurate approximation to the zero.

7  Accuracy

8  Parallelism and Performance

9  Further Comments

10  Example

10.1  Program Text

Program Text (c05ayce.c)

10.2  Program Data

10.3  Program Results

Program Results (c05ayce.r)