bisection algorithm

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bisection algorithm

[′bī‚sek·shən ′al·gə‚rith·əm]
(mathematics)
A procedure for determining the root of a function to any desired accuracy by repeatedly dividing a test interval in half and then determining in which half the value of the function changes sign.
McGraw-Hill Dictionary of Scientific & Technical Terms, 6E, Copyright © 2003 by The McGraw-Hill Companies, Inc.
References in periodicals archive ?
According to the abovementioned algorithm 1, the transmission power [P.sup.(s,0).sub.i,j] and [P.sup.(s,1).sub.i,j] in Theorem 2 and 3 should be obtained by using bisection method with the complexity o([2log.sub.2] ([delta])), where [delta] is the required accuracy.
The bisection method for root-finding applied to (4.1) starts with an initial guess for an interval [x-, x+] containing the root x, and iteratively updates this interval via
A bisection method can be taken to recursively search for the minimum feasible value of [tau].
The method is a root-finding algorithm combining the bisection method, the secant method, and inverse quadratic interpolation which has the advantage of fast-converging.
If one of the tests showed a pullout failure (Figure 8(a)) and the other one a tensile failure (Figure 8(b)), the development length laid in the interval and had to be found by further tests using the interval bisection method. If not, the bond length was increased (in case of two pullout failures) or decreased (in case of two tensile failures) again, until each failure mode had occurred once.
We solve by bisection method to find [R.sup.*] = R.
In the work of Trayner and Glowacki [13] the Saha equation for the situation of ideal plasma with single element species was firstly reformulated into a one-dimensional equation and then solved with some numerical algorithm such as the bisection method. Later, Zaghloul extended this method for the situation of nonideal plasma with multielement species while maintaining the one dimensionality of the method [12].
Using the bisection method, the temperature of each cell can be determined by the energy-temperature list.
In this paper, we choose a simple bisection method. For any selected rectangle [mathematical expression not reproducible], this branching rule is given as follows:
We can see from the bisection method that, for given r, the inner optimization problem is transformed into the problem of minimizing the total transmit power: