1 citations · 1 across the 2 of their papers we have counts for
5 papers
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…
Analysis of the multiplicative Schwarz method for matrices with a special block structure
Carlos Echeverría, Jörg Liesen, Petr Tichý
We analyze the convergence of the (algebraic) multiplicative Schwarz method applied to linear algebraic systems with matrices having a special block structure that arises, for exam…
Max-min and min-max approximation problems for normal matrices revisited
Jörg Liesen, Petr Tichý
We give a new proof for an equality of certain max-min and min-max approximation problems involving normal matrices. The previously published proofs of this equality apply tools fr…
Characterization of worst-case GMRES
Vance Faber, Jörg Liesen, Petr Tichý
Given a matrix and iteration step , we study a best possible attainable upper bound on the GMRES residual norm that does not depend on the initial vector . This quantity…
The field of values bound on ideal GMRES
Jörg Liesen, Petr Tichý
A widely known result of Elman, and its improvements due to Starke, Eiermann and Ernst, gives a bound on the worst-case GMRES residual norm using quantities related to the field of…