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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
where = is the reduced Planck constant.. The quintessentially quantum mechanical uncertainty principle comes in many forms other than position–momentum. The energy–time relationship is widely used to relate quantum state lifetime to measured energy widths but its formal derivation is fraught with confusing issues about the nature of time.
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.
False position and regula falsi are often treated as names for the same algorithm or class of algorithms. Yes, I don't deny that, and I concede that Wikipedia's policy is not to promote new usages. But, as you said, both names are widely-used and well-established. That means that Wikipedia isn't compelled to use one instead of the other.
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The following other wikis use this file: Usage on de.wikipedia.org Regula falsi; Usage on de.wikibooks.org Ing Mathematik: Numerisches Lösen nichtlinearer Gleichungen
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