The Infona portal uses cookies, i.e. strings of text saved by a browser on the user's device. The portal can access those files and use them to remember the user's data, such as their chosen settings (screen view, interface language, etc.), or their login data. By using the Infona portal the user accepts automatic saving and using this information for portal operation purposes. More information on the subject can be found in the Privacy Policy and Terms of Service. By closing this window the user confirms that they have read the information on cookie usage, and they accept the privacy policy and the way cookies are used by the portal. You can change the cookie settings in your browser.
One possible approach to the solution of large sparse linear systems is to reorder the system matrix to bordered block diagonal form and then to solve the block system in parallel. We consider the duality between singly bordered and doubly bordered block diagonal forms. The idea of a stabilized doubly bordered block diagonal form is introduced. We show how a stable factorization of a singly bordered block diagonal matrix results in a stabilized doubly bordered block diagonal matrix. We propose using matrix stretching to generate a singly bordered form from a doubly bordered form. Matrix stretching is compared with two alternative methods for obtaining a singly bordered form and is shown to be efficient both in computation time and the quality of the resulting block structure.