DiscreteValueIteration.jl
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VI should use linear algebra by default.
Currently this package has two solvers: ValueIterationSolver and SparseValueIterationSolver. The SparseValueIteration solver converts the problem to matrices and then uses linear algebra to solve. This is faster for almost all cases, so it should probably be the default.
The only reason that you would not want to do this is if you couldn't fit the (sparse) matrices in memory.