Abstract
AbstractIn this paper, we are concerned with the inversion of circulant matrices and their quantized tensor‐train (QTT) structure. In particular, we show that the inverse of a complex circulant matrix , generated by the first column of the form admits a QTT representation with the QTT ranks bounded by . Under certain assumptions on the entries of , we also derive an explicit QTT representation of . The latter can be used, for instance, to overcome stability issues arising when numerically solving differential equations with periodic boundary conditions in the QTT format.
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