论文标题
部分可观测时空混沌系统的无模型预测
SpecSolve: Spectral methods for spectral measures
论文作者
论文摘要
具有连续光谱的无限维空间上的自动伴侣操作员很丰富，但没有特征性的基础。相反，通过光谱措施实现对角度化。 The SpecSolve package [SIAM Rev., 63(3) (2021), pp. 489--524] computes spectral measures of general (self-adjoint) differential and integral operators by combining state-of-the-art adaptive spectral methods with an efficient resolvent-based strategy. The algorithm achieves arbitrarily high orders of convergence in terms of a smoothing parameter, allowing computation of both discrete and continuous spectral components.本文将规格扩展到两个重要类的操作员：奇异的插图差异操作员和一般操作员铅笔。 Essential computational steps are performed with off-the-shelf spectral methods, including spectral methods on the real line, the ultraspherical spectral method, Chebyshev and Fourier spectral methods, and the ($hp$-adaptive and sparse) ultraspherical spectral element method.该集合说明了Specsolve的“离散化 - 合理”范式的功能和灵活性。
Self-adjoint operators on infinite-dimensional spaces with continuous spectra are abundant but do not possess a basis of eigenfunctions. Rather, diagonalization is achieved through spectral measures. The SpecSolve package [SIAM Rev., 63(3) (2021), pp. 489--524] computes spectral measures of general (self-adjoint) differential and integral operators by combining state-of-the-art adaptive spectral methods with an efficient resolvent-based strategy. The algorithm achieves arbitrarily high orders of convergence in terms of a smoothing parameter, allowing computation of both discrete and continuous spectral components. This article extends SpecSolve to two important classes of operators: singular integro-differential operators and general operator pencils. Essential computational steps are performed with off-the-shelf spectral methods, including spectral methods on the real line, the ultraspherical spectral method, Chebyshev and Fourier spectral methods, and the ($hp$-adaptive and sparse) ultraspherical spectral element method. This collection illustrates the power and flexibility of SpecSolve's "discretization-oblivious" paradigm.
