Disposition
•1. Presentation of the CG-METHOD
•2. Applications of the CG-METHOD
•3. Biography Stiefel
•4. Biography Hestenes
•5. Birth of the CG-METHOD at the Institut für Angewandte Mathematik  IAM, ETHZ
•6. Birth of the CG-METHOD at the Institute for Numerical Analysis INA, UCLA
•7. Final remarks
1
Although my talk should be understandable also for the nonspecialist I think that I have to try to explain briefly what is the cg-method. The best time for this is probably at the beginning when you are not yet too tired of my speech. The famous German mathematician David Hilbert once said. "A mathematical theory is not to be considered complete until you have made it so clear that you can explain it to the first man whom you meet on the street."  At his time women apparently ere ot supposed to be encountered on the street. Since the cg-method is theoretically fully clarified for at least fifty years, I am encouraged to undertake its popularization.
Of the different ways in which it can be presented I shall use the one Stiefel developed at the IAM. Hestenes derivation which he established independently is based more on geometrical considerations and will not be given here. Then I want to mention briefly some of the fields in which this method is applied.
Since this symposium is also meant to honor the brilliant inventors of the method short biographies of Stiefel and Hestenes will follow.
Based on my personal memories complemented by what I have found in some documents I shall show and comment next some drawings and pictures of the persons who participated in the birth of the method at the two institutes.

At the end I shall wrap up  my presentation with a few general remarks and acknowledgements for the help I received when preparing it.