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The explicit benefit of Gegenbauer reconstruction to eliminate Gibbs artifacts has been understood for nearly two decades. But an accompanying implicit benefit is the ability to significantly compress source data prior to reconstruction. Unfortunately, the choice of Gegenbauer reconstruction parameters is limited by regions of numerical instability as either parameter, lambda or m, increases. Prior studies assumed lambda and m to be linearly tied to N and then characterized the bounds of instability as well as recommended safe reconstruction parameter combinations. Subsequent work demonstrated how to predict source data analyticity, of which apriori knowledge is required to minimize reconstruction error.
This thesis complements such previous studies and recommends new Gegenbauer reconstruction parameter guidelines based on a suite of parameter optimizations spanning seven unique objectives. The first three of these objectives are achieved using asymptotic analysis while the remaining four are met using traditional numerical objective minimization techniques.
For further information please contact: mittelmann@asu.edu