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- W3125048870 abstract "The Collatz–Wielandt formula obtained by Lothar Collatz (1942) and Helmut Wielandt (1950) provides a simple variational characterization of the Perron–Frobenius eigenvalue of certain types of matrices. We introduce a nonlinear generalization of the Collatz–Wielandt formula and show that it enables finding the so-called maximal saddle-node bifurcations of systems of nonlinear equations. As a consequence, we obtain an easily verifiable criterion for the detection of such saddle-node bifurcations. We illustrate our approach by examples of finite-difference approximations of nonlinear partial differential equations and a system of power flow." @default.
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- W3125048870 date "2021-01-01" @default.
- W3125048870 modified "2023-09-25" @default.
- W3125048870 title "Finding Saddle-Node Bifurcations via a Nonlinear Generalized Collatz–Wielandt Formula" @default.
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- W3125048870 doi "https://doi.org/10.1142/s0218127421500085" @default.
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