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Local Linear Convergence of ISTA and FISTA on the LASSO Problem
We establish local linear convergence bounds for the ISTA and FISTA
iterations on the model LASSO problem. We show that FISTA can be viewed as an
accelerated ISTA process. Using a spectral analysis, we show that, when close
enough to the solution, both iterations converge linearly, but FISTA slows down
compared to ISTA, making it advantageous to switch to ISTA toward the end of
the iteration processs. We illustrate the results with some synthetic numerical
examples
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