BackgroundAgainst a backdrop of changing concepts of aid effectiveness, development effectiveness, health systems strengthening, and increasing emphasis on impact evaluation, this article proposes a theory-driven impact evaluation framework to gauge the effect of aid effectiveness principles on programmatic outcomes of different aid funded programs in the health sector of a particular country.MethodsThe foundation and step-by-step process of implementing the framework are described.ResultsWith empirical evidence from the field, the steps involve analysis of context, program designs, implementation mechanisms, outcomes, synthesis, and interpretation of findings through the programs’ underlying program theories and interactions with the state context and health system.ConclusionsThe framework can be useful for comparatively evaluating different aid interventions both in fragile and non-fragile state contexts.

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Power method is frequently used for finding largest Eigen-pair. On the other hand, Inverse Power method is utilized to find smallest Eigen-pair. Using shifting property, Power method and/or Inverse Power method can be used to find out other desired Eigen pairs too. Several lemmas based on Power method with shifting property are presented here. Moreover, a Modified Hybrid Iterative Algorithm based upon both Power method and Inverse Power method is proposed to find both largest and smallest Eigen-pairs simultaneously with ease. Several experiments have been performed to investigate the robustness and effectiveness of the algorithm. The proposed algorithm is able to find both (largest and smallest) Eigen-pairs successfully and efficiently. Moreover, the proposed algorithm is able to find out the nature (positive and negative sign) of the Eigen values and in some cases the algorithm is also able to find out the second largest Eigen pair in consequence.

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