Enhancing convergence performance

For models described by a set of ordinary differential equations there are a few modifications we may consider implementing that enhance the performance (robustness) of the Gauss-Newton method. The issues that one needs to address more carefully are (i) numerical instability during the integration of the state and sensitivity equations, (ii) ways to enlarge the region of convergence. 

Each vendor of SPICE simulation software has added features such as Monte Carlo analysis, schematic entry, and post simulation waveform processing, as well as extensive model libraries. In most cases, the manufacturers have modified the algorithms for controlling convergence and have added new parameters or syntax for component models. As a result, each electronic design automaton (EDA) tool vendor has the basic Berkeley SPICE 2 features and a unique set of capabilities and performance enhancements. 

The question of what influences variance in MEP performance is of obvious importance. From a network perspective, a crucial predictor of system performance is system structure. Future research should examine the relationship between the structure of MEPs and their relative performance. It could be hypothesized, for example, that MEPs with denser network structures will outperform those with sparser network structures because network density can increase the flow of information and resources and enhance trust and coordination among system members. There is convergent support for this line of reasoning from prior work on human groups in the laboratory (Shaw, 1964), social capital in human communities (e.g., Coleman, 1988), and work on the U.S. auto industry (Gulati Lawrence, 1999). 

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