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:
“Cardinal Mazarin was a great knave, but no great man; much more cunning than able; scandalously false and dirtily greedy.”
—Philip Dormer Stanhope, 4th Earl Chesterfield (1694–1773)
“They who say that women do not desire the right of suffrage, that they prefer masculine domination to self-government, falsify every page of history, every fact in human experience. It has taken the whole power of the civil and canon law to hold woman in the subordinate position which it is said she willingly accepts.”
—Elizabeth Cady Stanton (1815–1902)
“The method of painting is the natural growth out of a need. I want to express my feelings rather than illustrate them. Technique is just a means of arriving at a statement.... I can control the flow of paint: there is no accident, just as there is no beginning and no end.”
—Jackson Pollock (1912–1956)