External motivations for change in indefinite systems

This chapter turns to external motivations for changes in the licensing conditions of indefinites and in their series formation. It is shown by means of selected examples that language contact is not so much responsible for triggering the quantifier or free-choice cycles, but rather that the distribution of individual indefinites as well as of entire series may be influenced by patterns in contact languages. This may lead for instance to the imposition of negative concord, or the restructuring of an entire indefinite system after the model of a contact language. The chapter furthermore addresses the role of variation within the diasystem of one language for the advancement of changes affecting indefinites in the scope of negation.

A Convergence Analysis of the MINRES Method for Some Hermitian Indefinite Systems

Some convergence bounds of the minimal residual (MINRES) method are studied when the method is applied for solving Hermitian indefinite linear systems. The matrices of these linear systems are supposed to have some properties so that their spectra are all clustered around ±1. New convergence bounds depending on the spectrum of the coefficient matrix are presented. Some numerical experiments are shown to demonstrate our theoretical results.