NAG Library Function Document

nag_zero_cont_func_brent (c05ayc)

1

Purpose

2

Specification

3

Description

4

References

5

Arguments

1:    $\mathbf{a}$ – doubleInput

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

2:    $\mathbf{b}$ – doubleInput

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

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

3:    $\mathbf{eps}$ – doubleInput

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

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

4:    $\mathbf{eta}$ – 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:    $\mathbf{f}$ – 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:    $\mathbf{x}$ – doubleInput

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

2:    $\mathbf{comm}$ – 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 3.3.1.1 in How to Use the NAG Library and its Documentation).

Note: f should not return floating-point NaN (Not a Number) or infinity values, since these are not handled by nag_zero_cont_func_brent (c05ayc). If your code inadvertently does return any NaNs or infinities, nag_zero_cont_func_brent (c05ayc) is likely to produce unexpected results.

6:    $\mathbf{x}$ – 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:    $\mathbf{comm}$ – Nag_Comm *

The NAG communication argument (see Section 3.3.1.1 in How to Use the NAG Library and its Documentation).

8:    $\mathbf{fail}$ – NagError *Input/Output

The NAG error argument (see Section 3.7 in How to Use the NAG Library and its Documentation).

6

Error Indicators and Warnings

NE_ALLOC_FAIL

Dynamic memory allocation failed.
See Section 2.3.1.2 in How to Use the NAG Library and its Documentation for further information.

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.
See Section 2.7.6 in How to Use the NAG Library and its Documentation for further information.

NE_NO_LICENCE

Your licence key may have expired or may not have been installed correctly.
See Section 2.7.5 in How to Use the NAG Library and its Documentation for further information.

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)