FUNCTIONAL ROOT ALGORITHMS FOR TRANSCENDENTAL EQUATIONS
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Date
2024
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Abstract
By employing tangent functions, a class of root-finding algorithms is generated in its most general form. Sample algorithms corresponding to special forms of the functions are given next. The functional algorithms involve only first order derivatives and are generalizations of the Newton-Raphson method with the same quadratic order of convergence. Some special functional algorithms employing second order derivatives are also presented with cubic order of convergence. The algorithms are numerically tested and compared with the Newton-Raphson method. The advantages and the disadvantages as well as some criteria on how to select a suitable function is discussed. It is shown that by selecting an appropriate functional form, the number of iterations can be reduced and/or range of convergence interval can be increased. © 2024, Institute of Applied Mathematics of Baku State University. All rights reserved.