Summary
For a differential operatorL as defined in (2.1) we consider the eigenvalue problemL u=λu and describe a method to obtain a pointwise bound Ψ≧|u−v| wherev denotes the Rayleigh-Ritz approximation to an exact eigenfunctionu. The upper bound Ψ is continuous, but only piecewise differentiable and calculated by solving certain (inverse-positive!) auxiliary problems.
Our method uses well-known estimations for Ψ(t i) at a finite number of pointst i∈[a, b] to calculate an upper, bound in the whole interval [a, b].
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The author would like to, thank the Battelle Institute Geneve for their assistance
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Küpper, T. Pointwise lower and upper bounds for eigenfunctions of ordinary differential operators. Numer. Math. 27, 111–119 (1976). https://doi.org/10.1007/BF01399089
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DOI: https://doi.org/10.1007/BF01399089