Summary.
A method is proposed for the solution of a secular equation, arising in modified symmetric eigenvalue problems and in several other areas. This equation has singularities which make the application of standard root-finding methods difficult. In order to solve the equation, a class of transformations of variables is considered, which transform the equation into one for which Newton's method converges from any point in a certain given interval. In addition, the form of the transformed equation suggests a convergence accelerating modification of Newton's method. The same ideas are applied to the secant method and numerical results are presented.
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Received July 1, 1994
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Melman, A. Numerical solution of a secular equation . Numer. Math. 69, 483–493 (1995). https://doi.org/10.1007/s002110050104
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DOI: https://doi.org/10.1007/s002110050104