This book does not aim to be a textbook on functional analysis or numerical mathematics; it simply seeks to demonstrate how a structural change has occurred in numerical mathematics in recent times. Through the use of large computing systems on one hand and abstract methods on the other, a picture of numerical mathematics has emerged that is significantly different from that of about 10 to 20 years ago. As in other areas of mathematics, there is also a strong tendency towards abstraction in numerical mathematics. At the same time, the boundaries between individual mathematical disciplines are becoming blurred. It is now difficult to say, for example, whether functional analysis belongs to so-called pure or so-called applied mathematics. Functional analysis serves as a foundation for large parts of both of these disciplines.