TECHNISCHER SYSTEME MAGDEBURG

The standard algorithms for dense matrices become expensive for large matrices, since the number of floating point operations often grows like n3. Therefore it is neces-sary to have data-sparse algorithms that use the problem-inherent structure to reduce the computational complexity. Data-sparse means that the matrix can be represented with much fewer than n2 storage. This is for instance the case for rank or tensor structured matrices. We have worked on new highly efficient algorithms for hierarchical matrices and ma-trices in tensor train matrix format. Here we will focus on one eigenvalue algorithm for symmetric matrices of both classes of data-sparse matrices. Let M ∈ Cn×n. Then the pair (λ, v) is called eigenpair if it fulfills the equation: Mv = λv. If M is real and symmetric, i.e., M = MT ∈ Rn×n, then λ ∈ R and v ∈ Rn. Hierarchical Matrices Hierarchical (H-)matrices, see [2], are a data-sparse representation of dense matri-ces. With the help of a hierarchical structure the matrix is partitioned into submatrices