ABSTRACT
The development of computer technology brought an unprecedented performance increase during the last five decades. Coming from a few hundreds of floating-point operations per second we will reach at the end of this decade more than a petaflop per second (PFLOPS). In the same time frame numerical research got a big impetus. We will show that the appearance of a new computer technology also changed numerical algorithms. This also will be true for the large machines of the petascale class. It may be that the petascale class of machines will force even larger changes in numerical paradigms. In the following we will give a short synopsis of the development of modern computer systems for numerical purposes together with mathematical methods which where developed and heavily used at the same time. This should show how architectures and algorithms correspond over time. Discussing technical issues of recent and future computer architectures we will try to anticipate the implications of petascale computers on algorithms. Further, we will make some remarks on the economical impact of petascale computing.
