We consider the solution of large linear systems with multiple right-hand sides using a block GMRES approach. We introduce a new algorithm that effectively handles the situation of almost rank deficient block generated by the block Arnoldi procedure and that enables the recycling of spectral information at restart. The first feature is inherited from an algorithm introduced by Robbé and Sadkane...

We propose assertion-consistency (AC) semi-lattices as suitable orders for the analysis of partial models. Such orders express semantic entailment, multiple-viewpoint and multiple-valued analysis, maintain internal consistency of reasoning, and subsume finite De Morgan lattices. We classify those orders that are finite and distributive and apply them to design an efficient algorithm for multipl...

The algebra of truth values for fuzzy sets of type-2 consists of all mappings from the unit interval into itself, with operations certain convolutions of these mappings with respect to pointwise max and min. This algebra generalizes the truth-value algebras of both type-1 and of interval-valued fuzzy sets, and has been studied rather extensively both from a theoretical and applied point of view...

We show a connection between the De Morgan formula size of a Boolean function f : {0, 1}n → {0, 1} and the noise stability of the function. Specifically, we prove that for 0 < p ≤ 1/2 it holds that NSp(f) ≥ 1− 2p √ L(f) · ‖f‖2 · (1− ‖f‖2) where NSp(f) is the noise stability of f with noise parameter p, ‖f‖ is the L2 norm of f , and L(f) is the De Morgan formula size of f . This result stems fro...