We propose a class of iteration methods searching the best approximately generalized polynomial, which has parallel computational function and converges to the exact solution quadratically. We first transform it into ...We propose a class of iteration methods searching the best approximately generalized polynomial, which has parallel computational function and converges to the exact solution quadratically. We first transform it into a special system of nonlinear equations with constraint, then by using to certain iteration method, we combine the two basic processes of the Remes method into a whole such that the iterative process of the system of nonlinear equations and the computation of the solution to the system of linear equations proceed alternately. A lot of numerical examples show that this method not only has good convergence property but also always converges to the exact solution of the problem accurately and rapidly for almost all initial approximations .展开更多
A further reformulation of Naive Set Comprehension related to that proposed in ＂Resolving Insolubilia： Internal Inconsistency and the Reform of Naive Set Comprehension＂ （2012） is possible in which contradiction i...A further reformulation of Naive Set Comprehension related to that proposed in ＂Resolving Insolubilia： Internal Inconsistency and the Reform of Naive Set Comprehension＂ （2012） is possible in which contradiction is averted not by excluding sets such as the Russell Set but rather by treating sentences resulting from instantiation of such sets as the Russell Set in their own descriptions as invalid. So the set of all sets that are not members of thernselves in this further revision is a valid set but the claim that that set is or is not a member of itself is not validly expressible. Such an approach to set comprehension results in a set ontology co-extensive with that permitted by the Naive Set Comprehension Principle itself. This approach （that may be called Revised Set Comprehension Ⅱ） has as strong a claim to consistency as that formulated in ＂Resolving Insolubilia： Internal Inconsistency and the Reform of Naive Set Comprehension.＂展开更多
文摘We propose a class of iteration methods searching the best approximately generalized polynomial, which has parallel computational function and converges to the exact solution quadratically. We first transform it into a special system of nonlinear equations with constraint, then by using to certain iteration method, we combine the two basic processes of the Remes method into a whole such that the iterative process of the system of nonlinear equations and the computation of the solution to the system of linear equations proceed alternately. A lot of numerical examples show that this method not only has good convergence property but also always converges to the exact solution of the problem accurately and rapidly for almost all initial approximations .
文摘A further reformulation of Naive Set Comprehension related to that proposed in ＂Resolving Insolubilia： Internal Inconsistency and the Reform of Naive Set Comprehension＂ （2012） is possible in which contradiction is averted not by excluding sets such as the Russell Set but rather by treating sentences resulting from instantiation of such sets as the Russell Set in their own descriptions as invalid. So the set of all sets that are not members of thernselves in this further revision is a valid set but the claim that that set is or is not a member of itself is not validly expressible. Such an approach to set comprehension results in a set ontology co-extensive with that permitted by the Naive Set Comprehension Principle itself. This approach （that may be called Revised Set Comprehension Ⅱ） has as strong a claim to consistency as that formulated in ＂Resolving Insolubilia： Internal Inconsistency and the Reform of Naive Set Comprehension.＂
