Institut für Numerische Simulation (INS): Browsing Institut für Numerische Simulation (INS) by Subject "error estimates"
Now showing items 1-4 of 4
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Convergence of generalized cross-validation for an ill-posed integral equation
Jahn, Tim (2023-12)In this article we rigorously show consistency of generalized cross-validation applied to an exemplary ill-posed integral equation, given a finite number of noisy point evaluations. In particular, we present non-asymptotic ... -
Efficient solution of ill-posed integral equations through averaging
Griebel, Michael; Jahn, Tim (2024-01)This paper discusses the error and cost aspects of ill-posed integral equations when given discrete noisy point evaluations on a fine grid. Standard solution methods usually employ discretization schemes that are directly ... -
On the numerical approximation of the Karhunen-Loève expansion for lognormal random fields
Michael Griebel; Guanglian Li (2019-07)The Karhunen-Loève (KL) expansion is a popular method for approximating random fields by transforming an infinite-dimensional stochastic domain into a finite-dimensional parameter space. Its numerical approximation is of ... -
On the numerical approximation of the Karhunen-Loève expansion for random fields with random discrete data
Griebel, Michael; Li, Guanglian; Rieger, Christian (2021-12)Many physical and mathematical models involve random fields in their input data. Examples are ordinary differential equations, partial differential equations and integro–differential equations with uncertainties in the ...