NAG Library Routine Document

F11GTF

1  Purpose

2  Specification

3  Description

4  References

5  Parameters

1:     ITN – INTEGEROutput

On exit: the number of iterations carried out by F11GSF.

2:     STPLHS – REAL (KIND=nag_wp)Output

On exit: the current value of the left-hand side of the termination criterion used by F11GSF.

3:     STPRHS – REAL (KIND=nag_wp)Output

On exit: the current value of the right-hand side of the termination criterion used by F11GSF.

4:     ANORM – REAL (KIND=nag_wp)Output

On exit: the norm ${‖A‖}_1={‖A‖}_{\infty }$ when either it has been supplied to F11GRF or it has been estimated by F11GSF (see also Sections 3 and 5 in F11GRF). Otherwise, $\mathbf{ANORM}=0.0$ is returned.

5:     SIGMAX – REAL (KIND=nag_wp)Output

On exit: the current estimate of the largest singular value ${\sigma }_1\left(\stackrel{-}{A}\right)$ of the preconditioned iteration matrix $\stackrel{-}{A}=E^{-1}A{E}^{-\mathrm{H}}$, when either it has been supplied to F11GRF or it has been estimated by F11GSF (see also Sections 3 and 5 in F11GRF). Note that if $\mathbf{ITS}<\mathbf{ITN}$ then SIGMAX contains the final estimate. If, on final exit from F11GSF, $\mathbf{ITS}=\mathbf{ITN}$, then the estimation of ${\sigma }_1\left(\stackrel{-}{A}\right)$ may have not converged: in this case you should look at the value returned in SIGERR. Otherwise, $\mathbf{SIGMAX}=0.0$ is returned.

6:     ITS – INTEGEROutput

On exit: the number of iterations employed so far in the computation of the estimate of ${\sigma }_1\left(\stackrel{-}{A}\right)$, the largest singular value of the preconditioned matrix $\stackrel{-}{A}=E^{-1}A{E}^{-\mathrm{H}}$, when ${\sigma }_1\left(\stackrel{-}{A}\right)$ has been estimated by F11GSF using the bisection method (see also Sections 3, 5 and 8 in F11GRF). Otherwise, $\mathbf{ITS}=0$ is returned.

7:     SIGERR – REAL (KIND=nag_wp)Output

On exit: if ${\sigma }_1\left(\stackrel{-}{A}\right)$ has been estimated by F11GSF using bisection,

$$\mathbf{SIGERR}=\max \left(\frac{\left|{\sigma }_1^{\left(k\right)}-{\sigma }_1^{\left(k-1\right)}\right|}{{\sigma }_1^{\left(k\right)}},\frac{\left|{\sigma }_1^{\left(k\right)}-{\sigma }_1^{\left(k-2\right)}\right|}{{\sigma }_1^{\left(k\right)}}\right)\text{,}$$

where $k=\mathbf{ITS}$ denotes the iteration number. The estimation has converged if $\mathbf{SIGERR}\le \mathbf{SIGTOL}$ where SIGTOL is an input parameter to F11GRF. Otherwise, $\mathbf{SIGERR}=0.0$ is returned.

8:     WORK(LWORK) – COMPLEX (KIND=nag_wp) arrayCommunication Array

On entry: the array WORK as returned by F11GSF (see also Section 3 in F11GSF).

9:     LWORK – INTEGERInput

On entry: the dimension of the array WORK as declared in the (sub)program from which F11GTF is called (see also Section 5 in F11GRF).

Constraint: $\mathbf{LWORK}\ge 120$.

Note:  although the minimum value of LWORK ensures the correct functioning of F11GTF, a larger value is required by the iterative solver F11GSF (see also Section 5 in F11GRF).

10:   IFAIL – INTEGERInput/Output

On entry: IFAIL must be set to $0$, $-1\text{ or }1$. If you are unfamiliar with this parameter you should refer to Section 3.3 in the Essential Introduction for details.

For environments where it might be inappropriate to halt program execution when an error is detected, the value $-1\text{ or }1$ is recommended. If the output of error messages is undesirable, then the value $1$ is recommended. Otherwise, if you are not familiar with this parameter, the recommended value is $0$. When the value $-\mathbf{1}\text{ or }\mathbf{1}$ is used it is essential to test the value of IFAIL on exit.

On exit: $\mathbf{IFAIL}=\mathbf{0}$ unless the routine detects an error or a warning has been flagged (see Section 6).

6  Error Indicators and Warnings

$\mathbf{IFAIL}=-i$

On entry, the $i$th argument had an illegal value.

$\mathbf{IFAIL}=1$

F11GTF has been called out of sequence. For example, the last call to F11GSF did not return $\mathbf{IREVCM}=3$ or $4$.

7  Accuracy

8  Further Comments

9  Example