Abstract. A semi-computable set S in a computable metric space need not be computable. However, in some cases, if S has certain topological properties, we can conclude that S is computable. It is known that if a semi-computable set S is a compact manifold with boundary, then the computability of ∂S implies the computability of S. In this paper we examine the case when S is a 1-manifold with boundary, not necessarily compact. We show that a similar result holds in this case under assumption that S has finitely many components.
We construct a QR factorization of a given centrosymmetric real matrix A into centrosymmetric real matrices Q and R. We describe in detail a Householder-type algorithm based on perplectic orthogonal block-reflectors to obtain such a factorization and demonstrate an application of this result to solving centrosymmetric linear systems of full rank.
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