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.

中文翻译：

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关于自伴问题的超球谱对称化方法

描述了一种机制，用于对称化超球面光谱方法的自伴问题。所得离散是对称的和带状的。提出了一种用于自伴算子的自适应频谱分解的算法。探索了几种应用，以证明对称器和自适应频谱分解的特性。