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 * The  Secant  command numerically approximates the roots of an algebraic function,  f, using a technique similar to Newton's method but without the need to evaluate the derivative of  function. * Given an expression  f  and an initial approximate  a, the  Secant  command computes a sequence,  =, of approximations to a root of  f, where  Ã‚  is the number of iterations taken to reach a stopping criterion. The  Secant  command is a shortcut for calling the  Roots  command with the  method=secant  option 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 number of applications. * It requires only one function evaluation per iteration, as compared with Newton’s method which requires two Disadvantages of secant method * It may not converge. * There is no guaranteed error bound for the computed iterates. * It is likely to have difficulty if f? (? ) = 0.This means the x-axis is tangent to the graph of y = f (x) at x = ?. * Newton’s 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 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 sold after considering the total costs and the total sales is 2. 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. 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 sampling  method, the switching time point’s calculation formulas  of  tangent  method  and  secant  method  are established.This paper analyses the precision  of  switching turn-on and turn-off time point, and compare these switching time points. Calculation results show that SPWM pulses generated by tangent  method  and  secant  method  are 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 problem or solution. Example 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: 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.