Regula falsi

In mathematics, the regula falsi, method of false position, or false position method is a very old method for solving an equation with one unknown; this method, in modified form, is still in use. In simple terms, the method is the trial and error technique of using test ("false") values for the variable and then adjusting the test value according to the outcome. This is sometimes also referred to as "guess and check". Versions of the method predate the advent of algebra and the use of equations. As an example, consider problem 26 in the Rhind papyrus, which asks for a solution of (written in modern notation) the equation x + x/4 = 15. This is solved by false position. First, guess that x = 4 to obtain, on the left, . This guess is a good choice since it produces an integer value. However, 4 is not the solution of the original equation, as it gives a value which is three times too small. To compensate, multiply x (currently set to 4) by 3 and substitute again to get , verifying that the solution is x = 12. Modern versions of the technique employ systematic ways of choosing new test values and are concerned with the questions of whether or not an approximation to a solution can be obtained, and if it can, how fast can the approximation be found. Two basic types of false position method can be distinguished historically, simple false position and double false position. Simple false position is aimed at solving problems involving direct proportion. Such problems can be written algebraically in the form: determine x such that if a and b are known. The method begins by using a test input value x′, and finding the corresponding output value b′ by multiplication: ax′ = b′. The correct answer is then found by proportional adjustment, x = b / b′ x′ . Double false position is aimed at solving more difficult problems that can be written algebraically in the form: determine x such that if it is known that Double false position is mathematically equivalent to linear interpolation.

About this result

This page is automatically generated and may contain information that is not correct, complete, up-to-date, or relevant to your search query. The same applies to every other page on this website. Please make sure to verify the information with EPFL's official sources.

Related concepts (5)

Related courses (2)

Related lectures (33)

ChE-312: Numerical methods

This course introduces students to modern computational and mathematical techniques for solving problems in chemistry and chemical engineering. The use of introduced numerical methods will be demonstr

MATH-250: Numerical analysis

Construction et analyse de méthodes numériques pour la solution de problèmes d'approximation, d'algèbre linéaire et d'analyse

In numerical analysis, Brent's method is a hybrid root-finding algorithm combining the bisection method, the secant method and inverse quadratic interpolation. It has the reliability of bisection but it can be as quick as some of the less-reliable methods. The algorithm tries to use the potentially fast-converging secant method or inverse quadratic interpolation if possible, but it falls back to the more robust bisection method if necessary. Brent's method is due to Richard Brent and builds on an earlier algorithm by Theodorus Dekker.

In mathematics, the bisection method is a root-finding method that applies to any continuous function for which one knows two values with opposite signs. The method consists of repeatedly bisecting the interval defined by these values and then selecting the subinterval in which the function changes sign, and therefore must contain a root. It is a very simple and robust method, but it is also relatively slow. Because of this, it is often used to obtain a rough approximation to a solution which is then used as a starting point for more rapidly converging methods.

Bracketing Methods: Bisection and Regula Falsi ChE-312: Numerical methods

Explores bisection and Regula Falsi bracketing methods for finding roots.

Bisection Method, Newton Method

Covers the Bisection Method and Newton Method for solving nonlinear equations using interval splitting and tangent lines.

Bisection, Stop Criteria MATH-250: Numerical analysis

Explains the bisection method for nonlinear equations and how to determine stop criteria.