I spent 2h yesterday evening surfing for "fun things to read". My theme was "what is new in numerical methods". This is what I found:
FROM RANDOM MATRICES TO STOCHASTIC OPERATORS (ALAN EDELMAN AND BRIAN D. SUTTON)
- Years ago, a quant that was working for me said: I am using random matrices to model my pricing. Now I feel better as there is a bridge from random matrices to good old numerical methods.
- I really put this here because it had hyper matrices. The truth is I have not looked into new numerical math libraries in ages but if I were to use one I would like it thave multi-dimensional matrices that I could slice and dice the way I would like. I am not sure this library is up to all that but it is used in the next article.
A Parallel Algorithm for solving BSDEs - Application to the pricing and hedging of American options (C´eline Labart)
- What I liked here is that the extrapolation polynomial is based on on a sparse polynomial chaos approximation. Not to mention that the rest of the work was nice, although all put together I really do not know how efficient the implementation is.
Parametric Optimal Design Of Uncertain Dynamical Systems (Joseph T. Hays)
- This is about optimizing noisy dynamic system modeled with polynomial chaos expansions.
A Tour of the Jungle of Approximate Dynamic Programming (Warren B. Powell)
- This is like an orthgonalized condensed version of the Dr. Powell's book
Solution of Large Systems of Equations Using Approximate Dynamic Programming Methods (Dimitri P. Bertsekas, Huizhen Yu)
- There seems to be a whole new universe out there of solving large systems approximately. I have no idea of the "rank" of this article but I liked the approach.
Automatic Differentiation methods in computational Dynamical Systems: invariant manifolds and normal forms (Àlex Haro)
- This actually pretty neat, it is about computing the "skeleton" of choatic systems
Optimization-based Approximate Dynamic Programming (Marek Petrik)
- This one is mixes many tricks (such as continuation). I will need more time to read through it.