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 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′(α) = 0. This means the x-axis is tangent to the graph of y = f (x) at x = α. * 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
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 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′(α) = 0. This means the x-axis is tangent to the graph of y = f (x) at x = α. * 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