Secant Methods Application

SUBMITTED TO sir sajid presentation on application of secant system April 16, 2013 MCS foremost sem - ROLL 31 to 40 s METHOD * TheSecant subordination numerically nigh(a)s the roots of an algebraic function,f, using a technique similar to northwards system nevertheless without the need to evaluate the derivative offunction. * accustomed an expressionfand an initial approximatea, theSecantcommand computes a sequence,=, of approximations to a root off, whereis the play of iterations taken to take a leak a stopping criterion. TheSecantcommand is a shortcut for calling the growcommand with the regularity=secant option Advantages of secant method * It converges at meteoric than a linear rate, so that it is much rapidly convergent than the bisection method. * It does non overtop use of the derivative of the function, something that is not gettable in a issuance of applications. * It requires further one function evaluation per iteration, as comp ard with Newtons method wh ich requires 2 Disadvantages of secant method * It may not converge. * There is no guaranteed error echo for the computed iterates. * It is likely to keep back difficulty if f? (? ) = 0.This means the x-axis is tangent to the graph of y = f (x) at x = ?. * Newtons method generalizes more slowly to new methods for solving simultaneous systems of nonlinear pars. APPLICATION OF SECANT METHOD 1. You are working for a start-up computer fabrication company and have been asked to happen the stripped-down number of computers that the shop forget have to sell to hold a profit. The equation that gives the token(prenominal) number of computers to be interchange after considering the integrality costs and the follow sales is 2. Use the secant method of purpose roots of equations to find the minimum number of computers that need to be interchange to make a profit.Conduct three iterations to count on the root of the above equation. Find the unconditional relative approximate er ror at the end of each iteration and the number of solid digits at least meliorate at the end of each iteration. 3. forthwith the most important application of secant method is to predicting the earthquake performance of structures. sozen has been attribute with having developed progenitor procedures. 4. Based on the sinusoidal pulse width intonation technology and regular samplingmethod, the electric switch time points unhurriedness formulasoftangentmethodandsecantmethodare established.This paper analyses the precisionof exchange turn-on and turn-off time point, and compare these switching time points. Calculation results show that SPWM pulses generated by tangentmethodandsecantmethodare closest to the pulse generated by natural sampling, the THD is also smaller than by regular sampling. 5. Secant method is apply to determine the optimal stage. ( maximize or minimize ) the problem or solution. caseful You are working for a start-up computer assembly company and have been asked to determine the minimum number of computers that the shop will have to sell to make a profit.The equation that gives the minimum number of Computers x to be sold after considering the total costs And the total sales is origin Use the Secant method of finding roots of equations to find * The minimum number of computers that need to be sold to make a profit. Conduct three iterations to sum up the root of the above equation. * Find the absolute relative approximate error at the end of each iteration, and * The number of significant digits at least correct at the end of each iteration.