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Strassen's algorithm (and other similar "faster than O(n^3)" algorithms simply haven't proven to be useful in practice, even for fairly large (e.g. 10000 by 10000 matrix times 10000 by 10000 matrix) matrix-matrix multiplies. This is mostly because memory bandwidth and access times rather than flops are the real driving factor in matrix multiplication times. In this case, you'd definitely want to take advantage of the sparsity of X in doing the matrix multiplications.
@Gilead, if you write out the KKT conditions, you'll get a polynomial system of equations which also can't be solved by local numerical methods. I'd hardly call a system of polynomial equations a "closed form" solution to the problem. You could apply Groebner basis methods to that system of equations, but in my opinion you'd be better off using the polynomial optimization approach of Gloptipoly or one of its competitors to solve the minimization problem.
The Veroni diagram is useful if you have a large collection of fixed points and are then going to find the nearest one of these fixed points for many other points, but the work to compute the Voroni diagram can't be amortized if you only need to do the nearest neighbor calculation once.
What makes you think that the underlying signal is differentiable? If it isn't, then why are you trying to find its derivative? it might be more appropriate to look at the average rate of change of the exchange rate over some fixed period of time. If that period is reasonably long compared to time between samples, then it should be relatively easy to get a smoothed average rate of change of the exchange rate. Another question you should probably be asking yourself is what significance the volume numbers have.
The smallest eigenvalue (or the real part of the eigenvalue with smallest real value) of a matrix is a nonconvex function of the matrix. Thus I would expect this to be a hard nonconvex optimization problem unless something special about the additional structure of your problem simplifies things.
Yes, I'm aware of that system, but it's not as common in the areas of applied mathematics that I work in. Since many of my papers have appeared in journals in disciplines outside of mathematics, I've adopted the more main stream culture, despite the fact that I'm blessed with a "B" name...
At many institutions, prior tenure track experience at another university is counted in the tenure clock. e.g. if you have four years of tenure track experience at university A and then start at university B, they may tell you that you have only 3 years to gain tenure at university B rather than the usual 7 years.
