NAG Library Function Document

nag_zero_cont_func_cntin (c05awc)

1

Purpose

2

Specification

3

Description

4

References

5

Arguments

1:    $\mathbf{x}$ – 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:    $\mathbf{eps}$ – 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:    $\mathbf{eta}$ – 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:    $\mathbf{f}$ – 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_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 3.3.1.1 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_cntin (c05awc). If your code inadvertently does return any NaNs or infinities, nag_zero_cont_func_cntin (c05awc) is likely to produce unexpected results.

5:    $\mathbf{nfmax}$ – 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:    $\mathbf{comm}$ – Nag_Comm *

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

7:    $\mathbf{fail}$ – 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_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.
See Section 2.7.6 in How to Use the NAG Library and its Documentation for further information.

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_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_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)