Computing Krylov iterates in the time of matrix multiplication

Vincent Neiger, Clément Pernet, Gilles Villard

Krylov methods rely on iterated matrix-vector products $A^k{u}_j$ for an $n\times n$ matrix $A$ and vectors $u_1,\dots ,u_m$. The space spanned by all iterates $A^k{u}_j$ admits a pa…