47 citations · 103 across the 9 of their papers we have counts for
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math.NA2013★ 13 cited
Hermite spectral method with hyperbolic cross approximations to high-dimensional parabolic PDEs
Xue Luo, Stephen S. -T. Yau
It is well-known that sparse grid algorithm has been widely accepted as an efficient tool to overcome the "curse of dimensionality" in some degree. In this note, we first give the…
math.OC2013★ 38 cited
Hermite spectral method to 1D forward Kolmogorov equation and its application to nonlinear filtering problems
Xue Luo, Stephen S. -T. Yau
In this paper, we investigate the Hermite spectral method (HSM) to numerically solve the forward Kolmogorov equation (FKE). A useful guideline of choosing the scaling factor of the…