Hi Costeanu, Cuchulainn,I'm currently implementing the RBF method, and I may have a slightly better experience with it as what you mentioned,though I admitt it is not straightforward and I'm not sure yet if I can consider it as viable or not.I'm just beginning, but here is what I have observed about the points you made:1) it's not really clear how many nodes we need, but we don't necessarily need a large number of them. On the contrary, the few papersin the Finance literature that talk about the subject tend to say that we don't need much more than 100 or 200 nodes. They say that due to its spectral nature, the convergence should be fast.I can confirm by experience that 100 or 200 nodes gives quite an accuract result. 2) yes, it tends to be more unstable as we use more nodes (and also much slower, due to the larger amount of time to solve the dense matrix).Some people say this can be improved a lot by using preconditioning technique. I haven't tried that yet.3) people may not use them with more than 1000 basis functions, but if the accuracy reached with 100 nodes is already very good, then this is not a worry.By the way, I read the chapter on Meshfree in Daniel's book as a starting point for my implementation. I don't really see where he says that Meshfree with 121 basisis compared with FDM with 121 meshs. I see 2 places where he talks about performance comparisons. One is a comparison within the Meshfree method, betweendifferent types of radial basis, with 121 meshs. The other one is really a comparison with FDM, but with the FDM having 500 nodes. I also wouldn't think it makesmuch sense to compare the two methods with the same number of nodes, since they have quite different behaviours in convergence and the meaning of a "node" is different.We need to compare at a fixed accuracy, or at a fixed runtime.4) Same thing for a comparison with Monte-Carlo, I don't see why we should compare them for the same number of nodes/simulations. As to the dimension problem, I have implementedthe RBF in 1 and 2 dimensions. I must say I find the method quite elegant for implementation, as the extension to many dimensions is particularly convenient. In 2 dimensions, I seem toneed a bit more nodes than in 1 dimension, but far from an exponential increase. So, at a given accuracy, although my RBF tends to lose against my FDM in 1 dimension, in 2 dimensions it startsbeing pretty efficient by comparison. Which brings one question, maybe more to Daniel. The nice runtime gain that you mention in your chapter on Meshfree, is it with the matrix inversion at every time steps or not?Because in a general situation, I think the matrix will be different at each time, such that it has to be inverted many times for 1 pricing. Then it seems slower than FDM to me. But if we take constantcoefficients and time steps, then the inversion can be done only once and the RBF can win. But that does not look like a realistic and interesting test case to me, as most of the time the interestrates, volatility, and time-steps, will not be constant.5) the choice of the colocation points indeed seem to be important and I'm not sure how to do that. I have tried several distributions: a regular lattice, a random draw with Sobol distribution, anda random draw following the true Log-Normal distribution. For a reason I do not understand, the Sobol distribution gives me the best results. As for the interpolation problem you mention, I thinkyour solution to it seems reasonnable. In order to keep a meaningful colocation distribution through time, we may want to re-interpolate to new colocation points a few times for a long-term pricingwith intermediate cash-flows.7) I am also wondering about the unit issue you mention for higher dimensions. Until now, my 2 spot dimensions were in the same "unit" as I considered them to be 2 spot equities with roughly thesame order of magnitude. In the example of a hybrid model, where the 2 factors have completely different meanings, we might have a problem with the definition of the radial functions. Although, solvingthis might not be so difficult. We could imagine always working in reduced variables that would have the same order of magnitude, such as an interest rate and the relative return of a spot equity. Or onecould also think of having different shape coefficients in each space direction.To share some more results and opinions, I would say that:1) the main problem from my point of view is the inversion of ill-conditioned dense matrices. First of all, this is a very slow process, second, it's unstable. Hopefully, the preconditioning fixes that.2) even if the RBF method was made to work in a stable and runtime-efficient way in practical situations, I still wouldn't see it as "getting the best of FD and Monte-Carlo". Indeed, you would stillhave to work out these tedious boundary condition issues, that are so easy to handle with Monte-Carlo, and especially for path-dependent options, I guess Monte-Carlo will remain much more convenient.