On multiplicative and Volterra minimization methods - Özyapıcı, Ali; Rıza, Mustafa; Bilgehan, Bülent; Bashirov, Agamirza (Springer US, 2014)
Theory and applications of multiplicative and Volterra calculi have been evolving rapidly over the recent years. As numerical minimization methods have a wide range of applications in science and engineering, the idea of the design of minimization methods based on multiplicative and Volterra calculi is self-evident. In this paper, the well-known Newton minimization method for one and two variables is developed in the frameworks of multiplicative and Volterra calculi. The efficiency of these proposed minimization methods is exposed by examples, and the results are compared with the original minimization method. One of the striking results of the proposed method is that the rate of convergence and the range of initial values are considerably larger compared to the original method.
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Keywords: Newton minimization, Computer Science; 41A25, Algorithms, Curve fitting, Multiplicative minimization; 65D15, Theory of Computation, Volterra calculus, Numerical Analysis; Numeric Computing, Multiplicative calculus; MATHEMATICS, APPLIED, CALCULUS