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We consider a new algorithm in light of the min-max Collatz-Wielandtformalism to compute the principal eigenvalue and the eigenvector(eigen-function) for a class of positive Perron-Frobenius-like operators. Suchoperators are natural generalizations of the usual nonnegative primitivematrices. These have nontrivial applications in PDE problems such as computingthe principal eigenvalue of Dirichlet Laplacian operators on general domains.We rigorously prove that for general initial data the corresponding numericaliterates converge globally to the unique principal eigenvalue with quadraticconvergence. We show that the quadratic convergence is sharp with compatibleupper and lower bounds. We demonstrate the effectiveness of the scheme viaseveral illustrative numerical examples.

A global quadratic speed-up for computing the principal eigenvalue of Perron-like operators