Low-rank Kronecker-product approximation to multi-dimensional nonlocal operators. Part II. HKT representation of certain operators
This article is the second part continuing Part I [16]. We apply the H-matrix techniques combined with the Kronecker tensor-product approximation to represent integral operators as well as certain functions F(A) of a discrete elliptic operator A in a hypercube (0, 1)(d) is an element of R-d in the case of a high spatial dimension d. We focus on the approximation of the operator-valued functions A(-sigma), sigma > 0, and sign(A) for a class of finite difference discretisations A is an element of R-N x N. The asymptotic complexity of our data-sparse representations can be estimated by O(n(p) log(q) n), p = 1, 2, with q independent of d, where n = N-1/d is the dimension of the discrete problem in one space direction.
kronecker tensor-product high spatial dimension hierarchical matrices sinc-interpolation sinc-quadrature