Numerical solution of a secular equation (Q1347038)

For solving a secular equation, which has singularities that make the application of standard root-finding methods difficult, a class of convexifying transformations of variables is considered, which transform the equation into one for which Newton's method converges for any point in a certain 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.