Quantifying uncertainty: innovations in high dimensional computation

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High dimensional problems (problems in which there are hundreds or thousands of continuous variables) arise in many applications, from ground water flow to mathematical physics and finance. They typically present major challenges to computational resources and serious mathematical challenges in devising new and improved methods and in proving that they are effective. The aim of this project is to develop new computational methods and theory for high dimensional problems, and to apply these methods to significant applications. The results are expected to allow faster and more accurate solution of problems of growing importance.