Application Robustification, a promising approach for reducing processor power, converts applications into numerical optimization problems and solves them using gradient descent and conjugate gradient algorithms . The improvement in robustness, however, comes at the expense of performance when compared to the baseline non-iterative versions of these applications. To mitigate the performance loss from robustification, we present the design of a hardware accelerator and corresponding software support that accelerate gradient descent and conjugate gradient based iterative implementation of applications. Unlike traditional accelerators, our design accelerates different types of linear algebra operations found in many algorithms and is capable of efficiently handling sparse matrices that arise in applications such as graph matching. We show that the proposed accelerator can provide significant speedups for iterative versions of several applications and that for some applications such as least squares, it can substantially improve the computation time as compared to the baseline non-iterative implementation.