Discrete Interpolation Norms with Applications

M Arioli, Daniel Loghin

Research output: Contribution to journalArticle

26 Citations (Scopus)


We describe norm representations for interpolation spaces generated by finite-dimensional subspaces of Hilbert spaces. These norms are products of integer and noninteger powers of the Grammian matrices associated with the generating pair of spaces for the interpolation space. We include a brief description of some of the algorithms which allow the efficient computation of matrix powers. We consider in some detail the case of fractional Sobolev spaces both for positive and negative indices together with applications arising in preconditioning techniques. Numerical experiments are included.
Original languageEnglish
Pages (from-to)2924-
JournalSIAM Journal on Numerical Analysis
Issue number4
Publication statusPublished - 1 Jan 2009


  • domain decomposition
  • interpolation spaces
  • finite element method
  • Hilbert spaces


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