Module oc_gmres_mod

1.

Purpose: generalized minimum-residual descent step

		      GMRES($\bold m,\bold R,\bold g,\bold G$)  {
		 		 $\b_i = -\frac{\left (\g^*\cdot\bold g_i\right )} {\left (\bold g_i^*\cdot\bold g_i\right )}$ $\left \{\begin{array}
{l} \bold g=\bold g+\sum\limits_1^{k-1}\b_i\bold g_i \\  \bold G=\bold G+\sum\limits_1^{k-1}\b_i\bold G_i\end{array}\right .$
		 		 $\c = \frac{\left (\g^*\cdot\g\right ) }{\left (\bold g_{k-1}^*\cdot\bold g_{k-1}\right )}$ 		$\left \{\begin{array}
{l} \bold s=\bold g+\c\bold s\\  \S=\bold G+\c\S \end{array}\right .$
		 		 $\alpha= -\frac{\left (\g^*\cdot\g\right ) }{\left (\S^*\cdot\S\right )}$ 		$\left \{\begin{array}
{l} \bold m=\bold m+\alpha\bold s\\  \bold R=\bold R+\alpha\S \end{array}\right .$ 
		 		 }

2.

Functions and subroutines

(a)

integer function oc_gmres(forget,x_,g_,rr_,gg_,s_,ss_,maxmem)

• forget: re-initialize operator
• x_: model file tag
• >_: gradient file tag
• rr_: residual file tag
• >g_: conjugate gradient file tag
• s_: previous step file tag
• ss_: conjugate previous step file tag

D