https://studylib.net/doc/25312294/wrc-537-
This paper sketches the main research developments in the area of computational methods for eigenvalue problems
during the 20th century. The earliest of such methods dates back to work of Jacobi in the middle of the 19th century.
Since computing eigenvalues and vectors is essentially more complicated than solving linear systems, it is not surprising
that highly signicant developments in this area started with the introduction of electronic computers around 1950. In
the early decades of this century, however, important theoretical developments had been made from which computational
techniques could grow. Research in this area of numerical linear algebra is very active, since there is a heavy demand for
solving complicated problems associated with stability and perturbation analysis for practical applications. For standard
problems, powerful tools are available, but there still remain many open problems. It is the intention of this contribution
to sketch the main developments of this century, especially as they relate to one another, and to give an impression of
the state of the art at the turn of our century. c 2000 Elsevier Science B.V. All rights reserved