I know the GMRES (Generalized minimal residual method) is a method to solve a system of equations Ax=b where A is non singular matrix of size m by m. My question what is restarted GMRES method ? Why is it used?
2026-04-22 01:22:54.1776820974
Why is restarted GMRES used?
62 Views Asked by Bumbble Comm https://math.techqa.club/user/bumbble-comm/detail At
1
GMRES builds up a basis where each vector is expected to have few zeros, which means it needs a lot of memory. In many problems we cannot even save $A$ as a matrix in the first place so it is impossible to store the complete basis.
A way to "solve" this problem is just using a fixed number of basis vectors, and as soon as you've used up those slots, you just delete them and begin over again, but with the current approximation. The convergence is obviously not guaranteed anymore, and in practice, this method often even leads to stagnation. But in many practical applications this is sufficient. (Or all you can hope for.)
(There are also other reasons to use restarted GMRES, but these are rather technical and usually very dependent on the actual problem.)