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[1905.06391] The Statistical Finite Element Method
The finite element method (FEM) is one of the great triumphs of modern day applied mathematics, numerical analysis and algorithm development. Engineering and the sciences benefit from the ability to simulate complex systems with FEM. At the same time the ability to obtain data by measurements from these complex systems, often through sensor networks, poses the question of how one systematically incorporates data into the FEM, consistently updating the finite element solution in the face of mathematical model misspecification with physical reality. This paper presents a statistical construction of FEM which goes beyond forward uncertainty propagation or solving inverse problems, and for the first time provides the means for the coherent synthesis of data and FEM.
numerical  pde  approximation_theory  statistics  applied_math  for_friends  spatio-temporal_statistics 
23 days ago by rvenkat
Nineteen Dubious Ways to Compute the Exponential of a Matrix, Twenty-Five Years Later
A wonderfully written article on the difficulty to compute in a general manner the matrix exponential
coink  numerical  recipe  matrix  exponential  math 
september 2019 by paunit

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