NAG Library Routine Document

F11GFF

1  Purpose

2  Specification

3  Description

4  References

5  Parameters

1:     ITN – INTEGEROutput

On exit: the number of iterations carried out by F11GEF.

2:     STPLHS – REAL (KIND=nag_wp)Output

On exit: the current value of the left-hand side of the termination criterion used by F11GEF.

3:     STPRHS – REAL (KIND=nag_wp)Output

On exit: the current value of the right-hand side of the termination criterion used by F11GEF.

4:     ANORM – REAL (KIND=nag_wp)Output

On exit: for CG and SYMMQ methods, the norm ${‖A‖}_1={‖A‖}_{\infty }$ when either it has been supplied to F11GDF or it has been estimated by F11GEF (see also Sections 3 and 5 in F11GDF). Otherwise, $\mathbf{ANORM}=0.0$ is returned.

For MINRES method, an estimate of the infinity norm of the preconditioned matrix operator.

5:     SIGMAX – REAL (KIND=nag_wp)Output

On exit: for CG and SYMMQ methods, the current estimate of the largest singular value ${\sigma }_1\left(\stackrel{-}{A}\right)$ of the preconditioned iteration matrix $\stackrel{-}{A}=E^{-1}A{E}^{-\mathrm{T}}$, when either it has been supplied to F11GDF or it has been estimated by F11GEF (see also Sections 3 and 5 in F11GDF). Note that if $\mathbf{ITS}<\mathbf{ITN}$ then SIGMAX contains the final estimate. If, on final exit from F11GEF, $\mathbf{ITS}=\mathbf{ITN}$, 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.

For MINRES method, an estimate of the final transformed residual.

6:     ITS – INTEGEROutput

On exit: for CG and SYMMQ methods, 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 $\stackrel{-}{A}=E^{-1}A{E}^{-\mathrm{T}}$, when ${\sigma }_1\left(\stackrel{-}{A}\right)$ has been estimated by F11GEF using the bisection method (see also Sections 3, 5 and 8 in F11GDF). Otherwise, $\mathbf{ITS}=0$ is returned.

7:     SIGERR – REAL (KIND=nag_wp)Output

On exit: for CG and SYMMQ methods, if ${\sigma }_1\left(\stackrel{-}{A}\right)$ has been estimated by F11GEF 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 F11GDF. Otherwise, $\mathbf{SIGERR}=0.0$ is returned.

For MINRES method, an estimate of the condition number of the preconditioned matrix.

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

On entry: the array WORK as returned by F11GEF (see also Section 3 in F11GEF).

9:     LWORK – INTEGERInput

On entry: the dimension of the array WORK as declared in the (sub)program from which F11GFF is called (see also Section 5 in F11GDF).

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

Note:  although the minimum value of LWORK ensures the correct functioning of F11GFF, a larger value is required by the iterative solver F11GEF (see also Section 5 in F11GDF).

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.

$\mathbf{IFAIL}=1$

F11GFF has been called out of sequence. For example, the last call to F11GEF did not return $\mathbf{IREVCM}=3$ or $4$.

7  Accuracy

8  Further Comments

9  Example