On symmetrizing the ultraspherical spectral method for self-adjoint problems
Journal of Computational Physics（2020）
Abstract
A mechanism is described to symmetrize the ultraspherical spectral method for self-adjoint problems. The resulting discretizations are symmetric and banded. An algorithm is presented for an adaptive spectral decomposition of self-adjoint operators. Several applications are explored to demonstrate the properties of the symmetrizer and the adaptive spectral decomposition.
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Key words
Spectral methods,Symmetric-definite and banded eigenvalue problems,Infinite-dimensional linear algebra
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