funcBisec  R Documentation 
Bisection function to find solutions of the key equation of the
informSCI
algorithm.
funcBisec(f_1, f_2, a, b, maxIter = 1000, tol = 1/10^3)
f_1 
Left side of the key equation as a function in one variable. 
f_2 
Right side of the key equation as a function in one variable. 
a 
A real value indicating the left bound of the search region.

b 
A real value indicating the right bound of the search region.

maxIter 
A positive integer defining the maximum number of iterations. 
tol 
A nonnegative numeric indicating the error tolerance. 
The function tries to find a solution of the key equation of the
informSCI
algorithm which is equivalent to determining the
intersection point of f_1
and f_2
.
The function uses the bisection method and tries to determine the root
of the function f_1f_2
. Note that by definition of the key equation
and the assumptions of the informSCI
algorithm f_1f_2
is
a continuous strictly increasing function. Because of the assumptions on
a
and b
f_1f_2
has a nonpositive function value in
point a
and nonnegative function value in point b
. Thus,
f_1f_2
has exactly one root in the closed interval [a,b]
.
The bisection method repeatedly halves the interval between a
and
b
. The function stops when the root is found or when the maximum
number of iterations is reached or when the interval is less than tol
.
Returns intersection point. In the case that no intersection point is found, the left side of the final interval is returned, rather than the midpoint. The returned point is a lower approximation of the solution of the key equation.
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