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Integration Preconditioning of Pseudospectral Operators. I. Basic Linear Operators
This paper develops a family of preconditioners for pseudospectral approximations of pth-order linear differential operators subject to various types of boundary conditions. The approximations are based on ultraspherical polynomials with special attention being paid to Legendre and Chebyshev polynomial methods based on Gauss--Lobatto quadrature points. The eigenvalue spectrum of the …