Secant Methods Application

SUBMITTED TO sir sajid foundation on application of second order April 16, 2013 MCS 1st sem &8212&8212&8212&8212&8212&8212&8212&8212&8212&8212&8212&8212&8212&8212&8212&8212- ROLL 31 to 40 SECANT METHOD * TheSecantcommand numerically approximates the root of an algebraic function,f, using a technique similar to Newtons method notwithstanding without the need to evaluate the derived offunction. * Given an expressionfand an initial approximatea, theSecantcommand computes a sequence,=, of approximations to a root off, whereis the numeral of iterations taken to r distributively a stopping criterion. TheSecantcommand is a shortcut for calling theRootscommand with themethod=secant picking Advantages of secant method * It converges at faster than a linear rate, so that it is more rapidly convergent than the bisection method. * It does not require use of the derivative of the function, something that is not available in a deed of applications. * It requires only single function evalu ation per iteration, as compared with Newtons method which requires cardinal Disadvantages of secant method * It may not converge. * There is no guaranteed demerit bound for the computed iterates. * It is likely to have difficulty if f? (? ) = 0.This means the x-axis is suntan to the graph of y = f (x) at x = ?. * Newtons method generalizes more easily to new methods for solving simultaneous systems of nonlinear equations. APPLICATION OF SECANT METHOD 1. You are working for a start-up estimator group company and have been asked to determine the token(prenominal) return of computers that the glom go away have to sell to confound a profit. The equation that gives the minimum number of computers to be sold after considering the fall costs and the gist sales is 2. Use the secant method of recovering grow of equations to find the minimum number of computers that need to be sold to make a profit.Conduct three iterations to estimate the root of the above equation. sustain t he absolute comparative approximate error at the last of from each one iteration and the number of significant digits at least correct at the end of each iteration. 3. Today the most important application of secant method is to predicting the quake performance of structures. sozen has been credited with having developed progenitor procedures. 4. Based on the sinusoidal pulse width modulation technology and regular samplingmethod, the shimmy succession points calculation formulasoftangentmethodandsecantmethodare established.This paper analyses the precisionofswitching 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 used to determine the optimal stage. ( maximize or minimize ) the job or solution. Example You are working for a start-up computer as sembly 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 Solution 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 estimate 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.