https://dudung.github.io/plaintext/tags/root-finding/Recent content in root-finding on plaintextHugo -- gohugo.ioenTue, 09 Jan 2024 05:14:00 +0800https://dudung.github.io/plaintext/0016/Tue, 09 Jan 2024 05:14:00 +0800https://dudung.github.io/plaintext/0016/intro intro Link to heading Regula-falsi method is one of the bracketing iterative method in finding roots of a non-linear equations, where the approximated root is found by using the straight lines and it is basto Bolzano’s theorem for continues functions (Yoweto 2020). After choose two initial guesses a line is formed using the two-point form of the line and by setting $y = 0$ an iterative formula is obtained (Weisstein, 2023).https://dudung.github.io/plaintext/0015/Mon, 08 Jan 2024 19:16:00 +0800https://dudung.github.io/plaintext/0015/intro formula flowchart algorithm problem code graphics challenges intro Link to heading If the derivative of function, whose root is to be found, does not exist or hard to find, secant method can be used instead of Newton raphson method, since it does not required the derivative but it requires two initial guesses for the roots (Mohan, 2021). Since this method retains only the most recent estimate, the root does not necessary bracketed (Weisstein).https://dudung.github.io/plaintext/0014/Mon, 08 Jan 2024 13:26:00 +0800https://dudung.github.io/plaintext/0014/intro formula flowchart algorithm problem code graphics challenges intro Link to heading The Newton-Raphson method is a method for finding succesively and quickly better approximation for the roots of a real-valued functions (Çapar, 2020). It is one of the most widely used methods for root finding and it can be shown that this technique is quadratically convergent as the root aproached (Smith, 1998). This algorithm is quite versatile with wide-ranging use cases than span many domains, e.https://dudung.github.io/plaintext/000v/Tue, 26 Dec 2023 07:04:00 +0800https://dudung.github.io/plaintext/000v/intro method example graphs results code challenges refs intro Link to heading The term graphical method related root finding might have lots of meanings as follow. The graphical method can also be presented in the form of perpendicular segements representing polynomial coefficients in the process of finding the real roots of pthe polynomial (Eisenberg, 1967). For complex roots the graphical method perform the analysis in the form of contour in complex plane (Pfeiffer, 1979).https://dudung.github.io/plaintext/000u/Sun, 24 Dec 2023 16:43:00 +0800https://dudung.github.io/plaintext/000u/intro example flowchart ⚠ algorithm ⚠ challenges refs intro Link to heading In mathematics a solution to an equation, that can be expressed as a number or an algebraic formula, is known as root (Britannica eds, 2023). Roots can be found algebraically as well as graphically, and the number of roots of a polynomial function gives the degree of the polynomial as shown by the fundamental theorem of algebra (Smith et al.https://dudung.github.io/plaintext/000s/Sat, 23 Dec 2023 20:27:00 +0800https://dudung.github.io/plaintext/000s/intro example flowchart algorithm code challenges refs intro Link to heading The simplest way to find a root of an equation is by scanning root candidates from an intial value, e.g. $x = x_a$, with increment $\Delta x$ until sign of the function change from previously ${\rm sign}(f(x_a))$, or if possible until $f(x) = 0$ (Rahmansyah & Ahhad, 2013). It is a typical solution in optics if met the physical limit of a resolution (Rom39, 2015).https://dudung.github.io/plaintext/0004/Tue, 12 Dec 2023 09:07:00 +0800https://dudung.github.io/plaintext/0004/intro root range method flowchart example graphics challenges refs intro Link to heading Bisection method pops up quite often when we talk about root finding methods due its very easy and simple algorithm to implement (Luna, 2020). This method uses the intermediate value theorem iteratively to find roots (Kong et al., 2020). It is also known as the interval halving method, where it provides a systematic approach to finding the root of a function within a given interval (Collimator, 2023).