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We present a family of numerical implementations of Kato's ODE propagatingglobal bases of analytically varying invariant subspaces, of which thefirst-order version is a surprising simple "greedy algorithm" that is bothstable and easy to program and the second-order version a relaxation of afirst-order scheme of Brin and Zumbrun. The method has application to numericalEvans function computations used to assess stability of traveling-wavesolutions of time-evolutionary PDE.

A local greedy algorithm and higher order extensions for global numerical continuation of analytically varying subspaces