Hi, today we'll going to learn the second method of numerical analysis the False Position Method out of 40 methods
FALSE POSITION METHOD
False Position Method is an alternative method and is more efficient then bisection method, it is the oldest method for finding the real root of an equation F( X ) = 0 and is similar to the bisection method.
Consider the equation F( X ) = 0 let [ X0 , X1 ] be two different values of X such that
F( X0 ) - F( X1 ) < 0.
OR
A simple modification of a secant method produces a method which is usually converges. the new method is called regula falsi (False Position) and also Linear interpolation.
it needs two initial approximations X0 and X1 so that F( X0 ) F( X1 ) < 0 i.e the two functions must have the opposite signs.
The Modified False Position Method
In this method the F( X ) value of a stagnant end point is halved if that point has repeated twice or more. the end point that repeats its called a stagnant point, the exception is to this rule is that for i = 2, the F( X ) value at one end is divided by 2 in immediately.
Stagnation is not desirable because it slows down convergence, particularly when the initial interval is very large or when the function deviates significantly from a straight line in the interval, the difficulty is avoided by the modified false position method which is explained above with picture.
Note: here is the link of examples keep practicing.
FALSE POSITION METHOD
False Position Method is an alternative method and is more efficient then bisection method, it is the oldest method for finding the real root of an equation F( X ) = 0 and is similar to the bisection method.
Consider the equation F( X ) = 0 let [ X0 , X1 ] be two different values of X such that
F( X0 ) - F( X1 ) < 0.
OR
A simple modification of a secant method produces a method which is usually converges. the new method is called regula falsi (False Position) and also Linear interpolation.
it needs two initial approximations X0 and X1 so that F( X0 ) F( X1 ) < 0 i.e the two functions must have the opposite signs.
The Modified False Position Method
In this method the F( X ) value of a stagnant end point is halved if that point has repeated twice or more. the end point that repeats its called a stagnant point, the exception is to this rule is that for i = 2, the F( X ) value at one end is divided by 2 in immediately.
Stagnation is not desirable because it slows down convergence, particularly when the initial interval is very large or when the function deviates significantly from a straight line in the interval, the difficulty is avoided by the modified false position method which is explained above with picture.
Note: here is the link of examples keep practicing.
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