ConceptSpectral Decomposition / 谱展开
Spectral Decomposition
A mathematical method that decomposes a linear operator into its eigenvalues and eigenfunctions. In Markov chain theory, it is used to solve the Poisson equation of the transition kernel. Analytic solutions are obtainable only when the target distribution has sufficiently simple structure, such as Gaussian distributions.
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Oct 9
A closed-form solution to the Poisson equation exists only when the transition kernel P has an analytically describable eigenfunction expansion or a known spectral decomposition.
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