Hierarchical tensor-product approximation to the inverse and related operators for high-dimensional elliptic problems
It is well known that integral operators in higher dimensions can be approximated by using the so-called hierarchical Kronecker tensor-product (HKT) format. The authors construct and analyze an HKT approximation for the general class of strongly positive operators defined as a sum of low-dimensional commutative operators and combine tensor product representation that includes one-dimensional operators. They develop a data sparse HKT approximation of the inverse of an elliptic operator as well as to the solution operator of the matrix Lyapunov-Sylvester equation. The approximation can be interpreted as an extension of the widely used fast Fourier transform.
scientific article; zbMATH DE number 2167500
scientific article