“Before starting to read everything on a new subject, I always try to think about it unbiased, and so I started with (probably) re-inventing the wheel.” -- Peter Sonneveld, speaking of the early development of IDR(s).
On February 2, the SIAM Student Chapter at TU Delft held a one-day workshop on Krylov subspace methods. The speakers, 12 PhD students in numerical linear algebra, gave overviews of their current work and its relation to Krylov subspaces. Participants came from different universities in the Netherlands and other European countries; among them were representatives of SIAM Student Chapters at Magdeburg, Manchester, and Prague.
Although Krylov methods are often associated with the iterative solution of large-scale linear systems, workshop participants described the application of Krylov subspaces in a wide variety of fields. Topics discussed included polynomial eigenvalue problems, estimation of matrix condition numbers, approximation of matrix functions, and applications in seismic wave propagation and flow control.
As the main speaker, Peter Sonneveld of TU Delft gave a historical talk about the development of the induced dimension reduction (IDR) method, a short-recurrence Krylov method for the efficient iterative solution of linear systems with general system matrices. In collaboration with Martin van Gijzen, Sonneveld has translated theoretical work he did in the 1980s into the IDR(s) algorithm.
More information on Krylov Day can be found here, and information on IDR(s) can be found here.
Participants at Krylov Day 2015.