Convergence Of Regula Falsi Method Pdf Download
Convergence of Regula Falsi Method
Regula Falsi, or the method of false position, is a numerical method for finding an approximate solution to f(x) = 0 on a finite interval [a, b], where f is a real-valued continuous function on [a, b] and satisfies f(a)f(b)
convergence of regula falsi method pdf download
Download Zip: https://www.google.com/url?q=https%3A%2F%2Ft.co%2FzoNYKENk0Y&sa=D&sntz=1&usg=AOvVaw3ydXbEDi47MyRZnrDZQVk1
The convergence of the Regula Falsi method has been studied by many researchers under various assumptions about the function f. Some of these assumptions include that both the first and second derivatives of f do not change sign on [a, b], or that f is convex or concave on [a, b]. However, these assumptions are not always satisfied by real-world problems, and may limit the applicability of the method.
In a recent paper by Trung Nguyen, the author proves the convergence of the Regula Falsi method for all continuous functions on [a, b] without any additional assumptions. The proof is based on a careful analysis of the ratio between the lengths of successive intervals generated by the method. The author shows that this ratio converges to zero as the number of iterations increases, implying that the sequence of approximations converges to a zero of f.
The paper also provides some numerical examples to illustrate the performance of the Regula Falsi method for different types of functions. The results show that the method can converge faster than other methods such as bisection or Newton's method in some cases, especially when f has multiple zeros or changes sign rapidly on [a, b].
If you are interested in learning more about the convergence of the Regula Falsi method and its applications, you can download a PDF version of the paper from [arXiv]. You can also find other related papers on numerical analysis from [arXiv], such as [A Modified Regula Falsi Method] by Dowell and Jarratt, or [The Convergence of Secant Methods for Nonlinear Equations] by Ostrowski.
I hope you enjoyed reading this article and found it useful. If you have any questions or feedback, please feel free to leave a comment below. Thank you for your attention!