Solving ordinary differential equations I (2nd revised. ed.): nonstiff problems
Solving ordinary differential equations I (2nd revised. ed.): nonstiff problems
The variational formulation of the Fokker-Planck equation
SIAM Journal on Mathematical Analysis
A Conjugate Points Theory for a Nonlinear Programming Problem
SIAM Journal on Control and Optimization
Matrices with banded inverses: inversion algorithms and factorization of Gauss-Markov processes
IEEE Transactions on Information Theory
Efficient and reliable schemes for nonlinear diffusion filtering
IEEE Transactions on Image Processing
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Nonlinear diffusion filtering presents a way to define and iterate Gaussian process regression so that large variance noise can be efficiently filtered from observations of size n in m iterations by performing approximately O(mn) number of multiplications, while at the same time preserving the edges of the signal. Experimental evidence indicates that the optimal stopping time exist and the steady state solutions obtained by setting m to an arbitrarily large number are suboptimal. This work discusses the Bayesian evidence criterion, gives an interpretation to its basic components and proposes an alternative, simple optimal stopping method. A synthetic large-scale example indicates the usefulness of the proposed stopping criterion.