Reducing energy consumption while providing performance and quality guarantees is crucial for computing systems ranging from battery-powered embedded systems to data centers. This paper considers approximate iterative applications executing on heterogeneous multi-core platforms under user-specified performance and quality targets. We note that allowing a slight yet bounded relaxation in solution quality can considerably reduce the required iteration count and thereby can save significant amounts of energy. To this end, this paper proposes Approx-RM , a resource management scheme that reduces energy expenditure while guaranteeing a specified performance as well as accuracy target. Approx-RM predicts the number of iterations required to meet the relaxed accuracy target at run-time. The time saved generates execution-time slack, which allows Approx-RM to allocate fewer resources on a heterogeneous multi-core platform in terms of DVFS, core type, and core count to save energy while meeting the performance target. Approx-RM contributes with lightweight methods for predicting the iteration count needed to meet the accuracy target and the resources needed to meet the performance target. Approx-RM uses the aforementioned predictions to allocate just enough resources to comply with quality of service constraints to save energy. Our evaluation shows energy savings of 31.6%, on average, compared to Race-to-idle when the accuracy is only relaxed by 1%. Approx-RM incurs timing and energy overheads of less than 0.1%.