György Bicsák, Dávid Sziroczák, Aaron Latty

Numerical methods


Regula Falsi Method

Regula Falsi, or False Position methods are a family of bracketing root finding methods, that can be thought of as an advanced version of the Bisection method. In the case of the Bisection method, the interval is always halved, and thus very little information is actually used from the function’s behaviour. The Regula Falsi relies on the calculation of the secant line of the function, and improving the root estimation based on the zero crossing of this secant line. This additional information results in more educated guessing than the bisection method, which increases the convergence rate of the algorithm, although at the expense of additional calculations. Similar to the bisection method, it requires an [a b] interval where the function crosses the 0 value for it to work.

Numerical methods

Tartalomjegyzék


Kiadó: Akadémiai Kiadó

Online megjelenés éve: 2019

ISBN: 978 963 454 283 4

This book on Numerical Methods is part of the Transportation and Vehicle Engineering Faculty’s curriculum at the Budapest University of Technology and Economics, created under the Stipendium Hungaricum Scholarship Programme. The book demonstrates the aim of developing and using numerical methods. Instead of relying on more complicated and expensive analytical solution methods, simpler arithmetical equations are used to approximate the accurate solution with the required level of accuracy. After discussing the various sources and propagation of solution errors, the book discusses the solution of single variable equations and system of equations. Following chapters describe the two main curve fitting methods; approximation and interpolation. These chapters are followed by the numerical differentiation and integration methods, then finally the numerical solutions for ordinary and partial differentiation equations are outlined. MATLAB is one of the most popular choice today for numerical computing, with its user friendly, yet powerful computing capability. It is practically an industry standard for prototyping and new developments, and there is great value for students to be introduced to solving problems with MATLAB. Many chapters in the notes show examples implemented in MATLAB, with actual working code available to use and practice.

Hivatkozás: https://mersz.hu/bicsak-numerical-methods//

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