The false position method or regula falsi method is a term for problem-solving methods in arithmetic, algebra, and calculus. In simple terms, these methods begin by attempting to evaluate a problem using test ("false") values for the variables, and then adjust the values accordingly.
Two basic types of false position method can be distinguished, 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. 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; for an affine linear function,
,
it provides the exact solution, while for a nonlinear function f it provides an approximation that can be successively improved by iteration.
Read more about False Position Method: Arithmetic and Algebra, Numerical Analysis, Analysis, Illinois Algorithm, Example Code
Famous quotes containing the words false, position and/or method:
“The wisest definition of poetry the poet will instantly prove false by setting aside its requisitions.”
—Henry David Thoreau (1817–1862)
“They aroused me to a determination to understand more fully the position of women, and the character of those men who talk so much of the need of our being “protected”Mremoving from us, meanwhile, what are often the very weapons of our defence [sic], occupations, and proper and encouraging remuneration.”
—Harriot K. Hunt (1805–1875)
“Steady labor with the hands, which engrosses the attention also, is unquestionably the best method of removing palaver and sentimentality out of one’s style, both of speaking and writing.”
—Henry David Thoreau (1817–1862)