| Abstract: |
| The classical weighted quadrature rules rely on roots of orthogonal polynomial and work well in context when the roots are well defined and real, e.g., in the case when the weight is positive definite. In this work, we present a method for quadrature construction that extends the weights that are negative but bounded from below. The asymptotic convergence rate of our method trails that of the classical Gauss-Legendre quadrature; however, in the pre-asymptotic regime our exotic construction vastly outperformed that classical approach, which is further magnified when applied to a multidimensional context, such as many application of (Uncertainty Quantification and radiation transport). |
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