An introduction to interpolation spaces and their applications from a numerical linear algebra perspective
by Mario Arioli, Cerfacs Researcher.
We will describe the theory of interpolation spaces with a focus both on Hilbert and on finite dimensional spaces. The finite dimensional framework clarifies several aspects of the theory, and its connections with matrix computations gives efficient algorithms for the solution of Steklov-Poincaré operators.
Interpolation spaces arise in several applications ranging from Domain Decomposition to CFD and finance modelling. We will give the finite element approximation of a few selected problems involving interpolation spaces from a numerical linear algebra perspective. Special attention will be given to Domain Decomposition method applications.
Finally, we will briefly describe several other applications where the above theory can be used to solve nonlocal operators.