# On the Numerical Approximation of the Karhunen-Loève Expansion for Random Fields with Random Discrete Data

@article{Griebel2021OnTN, title={On the Numerical Approximation of the Karhunen-Lo{\`e}ve Expansion for Random Fields with Random Discrete Data}, author={Michael Griebel and Guanglian Li and Christian Rieger}, journal={ArXiv}, year={2021}, volume={abs/2112.02526} }

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 coefficient functions described by random fields. They also play a dominant role in problems in machine learning. In this article, we do not assume to have knowledge of the moments or expansion terms of the random fields but we instead have only given discretized samples for them…

## One Citation

### A Dimension-adaptive Combination Technique for Uncertainty Quantification

- Computer Science, MathematicsArXiv
- 2022

An adaptive algorithm for the computation of quantities of interest involving the solution of a stochastic elliptic PDE where the diﬀusion coeﬃcient is parametrized by means of a Karhunen-Lo`eve expansion is presented and a dimension-adaptive combination technique is proposed.

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