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The following tables compares the various SG and SC methods, discussed on this website, against five important criteria: the rate of convergence when applied to systems exhibiting smooth solutions; the rate of convergence for rapidly-varying/discontinuous solutions; the ability to accurately simulate time variant systems; the number of random variables that can be modelled; and the algorithmic complexity.
| Method | Convergence: Smooth Solutions | Convergence: Discontinuous Problems | Time Variant Utility | Number of Dimensions | Algorithm Complexity |
|---|---|---|---|---|---|
| gPC SG | Exponential | Poor | Poor | Low | Simple |
| ME-gPC SG | Exponential | High-order | Good | Low | Hard |
| Weiner-Harr SG | Low-Order | Low-Order | Good | Low | Hard |
| p-adaptive SG | High-Order | Poor | Good | Moderate | hard |
| Tensor SC | Exponential | Poor | Poor | Low | Trivial |
| Isotropic Sparse Grid SC | Exponential | Poor | Poor | High | Moderate |
| Dimension Adaptive Sparse Grid SC | Exponential | High-Order | Good | High | Hard |
| Locally Adaptive Sparse Grid SC | Low-Order | Low-Order | Good | High | Hard |