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New error bounds for linear complementarity problems of weakly chained diagonally dominantB-matrices

100%
Sun D., Wang F.
Open Mathematics
|
2017
|
tom 15
|
nr 1
978-986
EN
Some new error bounds for the linear complementarity problems are obtained when the involved matrices are weakly chained diagonally dominant B-matrices. Numerical examples are given to show the effectiveness of the proposed bounds.
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An Inferentially Many-Valued Two-Dimensional Notion of Entailment

63%
Blasio C., Marcos J., Wansing H.
Bulletin of the Section of Logic
|
2017
|
tom 46
|
nr 3/4
EN
Starting from the notions of q-entailment and p-entailment, a two-dimensional notion of entailment is developed with respect to certain generalized q-matrices referred to as B-matrices. After showing that every purely monotonic singleconclusion consequence relation is characterized by a class of B-matrices with respect to q-entailment as well as with respect to p-entailment, it is observed that, as a result, every such consequence relation has an inferentially four-valued characterization. Next, the canonical form of B-entailment, a two-dimensional multiple-conclusion notion of entailment based on B-matrices, is introduced, providing a uniform framework for studying several different notions of entailment based on designation, antidesignation, and their complements. Moreover, the two-dimensional concept of a B-consequence relation is defined, and an abstract characterization of such relations by classes of B-matrices is obtained. Finally, a contribution to the study of inferential many-valuedness is made by generalizing Suszko’s Thesis and the corresponding reduction to show that any B-consequence relation is, in general, inferentially four-valued.
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