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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.
In numerical analysis, Ridders' method is a root-finding algorithm based on the false position method and the use of an exponential function to successively approximate a root of a continuous function (). The method is due to C. Ridders.
This may be helpful for example applying the false position method instead of a Newton iteration. It is easy to generate curves which are almost geometrically similar to the given implicit curve F ( x , y ) = 0 , {\displaystyle F(x,y)=0,} by just adding a small number: F ( x , y ) − c = 0 {\displaystyle F(x,y)-c=0} (see section #Smooth ...
The solutions were possibly, but not likely, arrived at by using the "method of false position", or regula falsi, where first a specific value is substituted into the left hand side of the equation, then the required arithmetic calculations are done, thirdly the result is compared to the right hand side of the equation, and finally the correct ...
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This means that the false position method always converges; however, only with a linear order of convergence. Bracketing with a super-linear order of convergence as the secant method can be attained with improvements to the false position method (see Regula falsi § Improvements in regula falsi) such as the ITP method or the Illinois method.