BRACKETING METHODS Flashcards
methods that exploit the fact that a function
typically changes sign in the vicinity of a root
Bracketing Method
A simple method for obtaining an estimate of the root of the equation f(x) 5 0 is to
make a plot of the function and observe where it crosses the x axis. This point, which
represents the x value for which f(x) 5 0, provides a rough approximation of the root.
Graphical Method
if f(xl) and f(xu) have opposite signs, there are an ____ number of roots in the interval
odd
if f(xl) and f(xu) have the same sign, there are either ______ or an _____ number of roots between the values.
no roots, even
There are two terms in the polynomial equal to zero.
Multiple root
capitalize on this observation by locating an interval where the function changes sign. Then the location of the sign change (and consequently,
the root) is identified more precisely by dividing the interval into a number of subintervals. Each of these subintervals is searched to locate the sign change. The process is repeated and the root estimate refined by dividing the subintervals into fIner increments.
Increment Search Method
Other terms for bisection method
Binary Chopping
Internal Halving
Bolzano’s Method
one type of incremental search method in which the interval is always divided in half. If a function changes sign over an interval, the function value at
the midpoint is evaluated. The location of the root is then determined as lying at the midpoint of the subinterval within which the sign change occurs. The process is repeated to obtain refined estimates.
Bisection Method
An alternative method that exploits this graphical insight is to join f(xl) and f(xu) by a straight line. The intersection of this line with the x axis represents an improved estimate of the root.
False-Position Method
Other term for False-Position Method
regula falsi
linear interpolation method
