Numerical solution of a secular equation |
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Authors: | A Melman |
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Institution: | (1) Department of Industrial Engineering and Management, Ben-Gurion University, IL-Beer-Sheva 84105, Israel Fax: 972-7-280776; e-mail: melman{\tt @}bgumail.bgu.ac.il , IL |
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Abstract: | 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.
Received July 1, 1994 |
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Keywords: | Mathematics Subject Classification (1991):65F15 65H05 |
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