Graeffe's method for eigenvalues |
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Authors: | G. Pólya |
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Affiliation: | (1) Department of Mathematics, Stanford University, 94305 Stanford, Calif., USA |
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Abstract: | Let an entire functionF(z) of finite genus have infinitely many zeros which are all positive, and take real values for realz. Then it is shown how to give two-sided bounds for all the zeros ofF in terms of the coefficients of the power series ofF, in fact in terms of the coefficients obtained byGraeffe's algorithm applied toF. A simple numerical illustration is given for a Bessel function. |
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