3-1 CHAPTER 3 ROOT FINDING This chapter is about different root searching techniques. Given a function f(x), we are interested to look for its root ξ(i.e. f(ξ) = 0). The general idea is to revise the value of x through a repeated process. The goal is for xto asymptotically approach ξas the number of iterations increases. Four iteration methods are considered: bisection, fixed-point iteration, Newton’s method, and secant method. Their basic concepts, algorithms, and implementations in Matlab are presented. In order to illustrate the relevancy of root finding to electrical engineering, we consider a diode circuit problem throughout this chapter. V0RivoltagexThe diode is governed by the diode equation: )1(/−=thVxSeIiwhere IS and Vthare known parameters of the device. We are interested to find the voltage xacross the diode. Since EE 3108 Semster B 2007/2008 S C Chan3-2 iRxV+=0, we have (by combining the two equations): )1(/0−=−thVxSeRIxV02105026.0/15=−+×∴−xex------(*) Thus, the problem is a root finding problem of the function 2105)(026.0/15−+×=−xexfx. The function is plotted below. 0.80.810.820.830.840.850.860.870.880.890.9−2−1012345We can observe from the graph that the root is 8596.0=ξ(4 s.f.). However, we need better methods because it is not effective to plot a graph for every problem.
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