Secant Methods Application

SUBMITTED TO sir sajid presentation on application of secant method April 16, 2013 MCS 1st sem - ROLL 31 to 40 SECANT method acting * The secantcommand numerically approximates the roots of an algebraic function,f, using a technique similar to Newtons method but without the need to evaluate the derivative offunction. * habituated an expressionfand an initial approximatea, theSecantcommand computes a sequence,=, of approximations to a root off, whereis the number of loopings taken to r individually a stopping criterion. TheSecantcommand is a shortcut for calling theRootscommand with themethod=secantoption Advantages of secant method * It converges at faster than a linear rate, so that it is more(prenominal) rapidly convergent than the bisection method. * It does not require use of the derivative of the function, something that is not available in a number of applications. * It requires only champion function evaluation per iteration, as compared with Newtons method which requires two Disadvantages of secant method * It may not converge. * There is no guaranteed error terpsichore for the computed iterates. * It is likely to mother difficulty if f? (? ) = 0.This means the x-axis is tangent to the graph of y = f (x) at x = ?. * Newtons method generalizes more easily to new methods for solving simultaneous systems of nonlinear compares. APPLICATION OF SECANT METHOD 1. You are functional 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 to be change after(prenominal) considering the total costs and the total sales is 2. Use the secant method of determination 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. date the absolute relative approximate error at the end of each iteration a nd 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 earthquake 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 transformation clip 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 little than by regular sampling. 5. Secant method is used to determine the optimal stage. ( maximize or minimize ) the problem or solution. Example You are working for a start-up computer assembly company and have been asked to determine the minimum number of compu ters 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.