3 papers
math.NA2025
On finite precision block Lanczos computations
Dorota Šimonová, Petr Tichý
In her seminal 1989 work, Greenbaum demonstrated that the results produced by the finite precision Lanczos algorithm after iterations can be interpreted as exact Lanczos result…
math.NA2025
Block CG algorithms revisited
Petr Tichý, Gérard Meurant, Dorota Šimonová
Our goal in this paper is to clarify the relationship between the block Lanczos and the block conjugate gradient (BCG) algorithms. Under the full rank assumption for the block vect…
math.NA2021
When does the Lanczos algorithm compute exactly?
Dorota Šimonová, Petr Tichý
In theory, the Lanczos algorithm generates an orthogonal basis of the corresponding Krylov subspace. However, in finite precision arithmetic, the orthogonality and linear independe…