As computers keeping advancing, many difficult problems which were unable to compute formerly now have the chance to get answered. It is always the goal of mathematicians and computer scientists to compute and get the answers of the linear systems. Since 1950s, there have been a lot of published papers discussing the issue. As the linear systems larger and larger, the computer efficiency required is higher and higher, so that it is very difficult to get the answers of large linear systems. Now, the problems are showing aurora. In this dissertation, several mathematical calculations to compute the linear systems will be discussed, as well as their background and theory. Moreover, they will also be practiced.

As we know, the theory about the linear equation AX−XB=C has already been well developed in the finite-dimensional cases. In this paper, we will try to extend it to infinite-dimensional cases by using a similar technique developed recently in the finite-dimensional case.

Thesis (doctoral)--Universität Basel, 1912. / Vita. Includes bibliographical references.

Thesis (doctoral)--K.B. Friedrich-Alexanders-Universität Erlangen, 1910. / Vita.

Thesis (doctoral)--Friedrich-Wilhelms-Universität zu Berlin, 1905. / Vita.

Thesis (doctoral)--Kgl. Ludwig-Maximilians-Universität zu München, 1914. / Vita.

Thesis (M.S.)--Naval Postgraduate School, 2002. / Thesis advisor(s): David Olwell, Samuel E. Buttrey. Includes bibliographical references (p. 79). Also available online.

Thesis (doctoral)--Albert-Ludwig-universität zu Freiburg im Breisgau, 1910. / Includes bibliographical references.

Thesis (Ph. D.)--Electrical and Computer Engineering, Georgia Institute of Technology, 2004. / Verriest, Erik, Committee Member ; Wardi, Yorai, Committee Member ; Yezzi, Anthony, Committee Member ; Wang, Yang, Committee Member ; Egerstedt, Magnus, Committee Chair. Vita. Includes bibliographical references (leaves 80-85).

Thesis--Copenhagen.