Finite-Precision Symmetric Krylov Methods: Exact Rounding Examples, Block Paige Identities,and a Variable-Block Lanczos Model

Short-recurrence Krylov methods that are equivalent in exact arithmetic often diverge in floating-point arithmetic. To illustrate this, we provide an exactly representable two-cycle for steepest descent with a recursively updated residual. A complementary convergence theorem gives a sufficient condi