Self-stabilizing iterative solvers

We show how to use the idea of self-stabilization, to make fault-tolerant iterative solvers. Generally, a self-stabilizing system is one that, starting from an arbitrary state (valid or invalid), reaches a valid state within a ~Anite number of steps. In this talk, We give two proof-of-concept exampless of self-stabilizing iterative linear solvers: one for steepest descent (SD) and one for conjugate gradients (CG). We will discuss convergence related properties and overhead of enforcing self-stabilization for conjugate gradient algorithm.