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Abstract: For a given nonlinear system, an observer that provides exactly linear error dynamics can be computed by solving the so-called Generalized Characteristic Equation (GCE). Unfortunately, existence of a solution to the GCE is not a generic property. We show how spline functions may be used to construct approximate solutions that minimize a norm of the nonlinear terms obstructing linearization of the error dynamics. The resulting error dynamics are shown to be locally exponentially stable. A numerical example illustrates the design and performance of the observer.