Modified Regula Falsi Method with Explanation l Algorithm l Example l and Matlab Code l Convergence

Описание: Modified Regula Falsi Method with Explanation l Algorithm l Example l and Matlab Code l Convergence
Regula falsi always converges, usually considerably faster than bisection method, there are situations that can slow its convergence. That problem isn't unique to regula falsi:
Other than bisection, all of the numerical equation-solving methods can have a slow-convergence or no-convergence problem under some conditions. Sometimes, Newton's method and the secant method diverge instead of converging – and often do so under the same conditions that slow regula falsi's convergence.
But, though regula falsi is one of the best methods, and even in its original un-improved version would often be the best choice; for example, when Newton's isn't used because the derivative is prohibitively time-consuming to evaluate, or when Newton's and Successive-Substitutions have failed to converge.
Regula falsi's failure mode is easy to detect:
The same end-point is retained twice in a row.
The problem is easily remedied by picking instead a modified false position, chosen to avoid slowdowns due to those relatively unusual unfavourable situations.

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