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We provide a simple analysis of the Douglas-Rachford splitting algorithm in the context of $\ell^1$ minimization with linear constraints, and quantify the asymptotic linear convergence rate in terms of principal angles between relevant vector spaces.
Numerical Methods for Computing Angles Between Linear Subspaces
Åke Björck and Gene H. Golub · 1973
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Sur l’approximation, par elements finis d’ordre un, et la resolution, par penalisation-dualité d’une classe de problemes de dirichlet non lineares
R. Glowinski and A. Marroco · 1975
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A dual algorithm for the solution of nonlinear variational problems via finite element approximation
D. Gabay and B. Mercier · 1976
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Splitting algorithms for the sum of two nonlinear operators
P. L. Lions and B. Mercier · 1979
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Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems
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A dual split Bregman method for fast ℓ 1 \ell^{1} minimization
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