Böcker av Wolfgang Hackbusch

Special numerical techniques are already needed to deal with n x n matrices for large n. Tensor data are of size n x n x...x n=nd, where nd exceeds the computer memory by far. Since standard methods fail, a particular tensor calculus is needed to treat such problems.

However, the technique of hierarchical matrices makes it possible to store matrices and to perform matrix operations approximately with almost linear cost and a controllable degree of approximation error.

This is the soft cover reprint of the very popular hardcover edition. The book offers a simultaneous presentation of the theory and of the numerical treatment of elliptic problems.

This book describes the methods by which tensors can be practically treated and shows how numerical operations can be performed. Applications include problems from quantum chemistry, approximation of multivariate functions, solution of pde and more.

Multi-grid methods are the most efficient tools for solving elliptic boundary value problems. One section describes special applications (convection-diffusion equations, singular perturbation problems, eigenvalue problems, etc.).