Finite precision block Lanczos computations

• Date: 12. 3. 2026
• Time: 14:00 - 15:30
• Address:
  Sokolovská 83, Praha
• Room: K3
• Speaker: Dorota Šimonová

The block Lanczos algorithm, a variant of the Lanczos algorithm operating with block vectors, is used in many applications, yet its behavior in finite precision arithmetic is not well understood. For the single-vector Lanczos algorithm, Greenbaum, building on the numerical analysis of Paige, presented a backward-like stable mathematical model of Lanczos computations. The basic idea is to construct a larger matrix from the one generated by finite precision computations whose eigenvalues lie in small intervals around those of the original matrix. An analogous construction can be defined for the block Lanczos algorithm; however, the absence of a block analogue of Paige's analysis complicates proving properties similar to those known in the single-vector case. Nevertheless, numerical experiments suggest that analogous properties may hold in practice.