A two-sided short-recurrence extended Krylov subspace method for nonsymmetric matrices and its relation to rational moment matching (Q2408146)

The author is concerned with the approximation of bilinear forms \(c^T f(A) b\), where \(A\) is a square matrix and \(b, c\) corresponding vectors. In this respect he considers extended Krylov subspaces, which correspond not only to positive but also to negative powers of the matrix \(A\), as these also give rise to a short recurrence for computing an orthonormal basis in the Hermitian case. Numerical experiments are also reported.