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Dong Zhang Zhenwei Guo Gang Wang Tongsong Jiang 《Mathematical Methods in the Applied Sciences》2020,43(6):3513-3523
Due to the rise of commutative quaternion in Hopfield neural networks, digital signal, and image processing, one encounters the approximate solution problems of the commutative quaternion linear equations and . This paper, by means of real representation and complex representation of commutative quaternion matrices, introduces concepts of norms of commutative quaternion matrices and derives two algebraic techniques for finding solutions of least squares problems in commutative quaternionic theory. 相似文献
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Zvonko Iljazović 《Mathematical Logic Quarterly》2020,66(1):51-64
We consider topological pairs , , which have computable type, which means that they have the following property: if X is a computable topological space and a topological imbedding such that and are semicomputable sets in X, then is a computable set in X. It is known, e.g., that has computable type if M is a compact manifold with boundary. In this paper we examine topological spaces called graphs and we show that we can in a natural way associate to each graph G a discrete subspace E so that has computable type. Furthermore, we use this result to conclude that certain noncompact semicomputable graphs in computable metric spaces are computable. 相似文献
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