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Simulation studies of our multivalued model have exhibited sharp error reductions for deeper searches using minimaxing.

A quite sharp error estimate between the approximate solution and the exact ones is obtained by choosing a suitable regularization parameter.

Both approaches rely on smooth solution reconstructions and may be used separately or in combination to obtain highly accurate solutions with asymptotically sharp error bounds.

Its natural expression, though commonly used, does not respect a sharp error bound: we here first prove the correctness of a second expression.

For a particular instance of the parameters under consideration, we are able to solve the underlying partial differential equations, compute an output, and give sharp error bounds.

This is mainly because they are easy in their construction and computer implementation and usually provide constant-free and sharp error estimates on the expense of losing the bounding property.

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Do authors expect a sharp error-catastrophe-like phase transition *in the absence* of horizontal gene transfer?

Sharp local error bounds are obtained for the solution of the linear autonomous Hamiltonian system considered in each time subinterval.

More recently, we have done some preliminary work on sharp a posteriori error estimates, error estimates and superconvergence of mixed finite element methods for optimal control problems (see, for example, [6 13]).

A sharper prediction-error histogram can be obtained from PE while HS can reduce embedding distortion.

Owing to our improvements, the sharper prediction-error histogram can be obtained for the reduction of embedding distortion.

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