Question
(a) Show that the iterative method xk+1 = xk1f(xk) xkf(xk1) f(xk) f(xk1) is mathematically equivalent to the secant method for solving a scalar nonlinear equation
(a) Show that the iterative method
xk+1 =
xk1f(xk) xkf(xk1)
f(xk) f(xk1)
is mathematically equivalent to the secant method for solving a scalar nonlinear equation f(x) = 0.
(b) When implemented in nite-precision oating-point arithmetic, what advantages or disadvantages
does the formula given in part (a) have compared with the formula for the secant method given in
Section 5.5.4?
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Step: 1
a To show that the iterative method given by xk1 xk1 fxk1 xk xk1 fxk fxk1 is mathematically equivalent to the secant method for solving the scalar non...
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Differential Equations and Linear Algebra
Authors: Jerry Farlow, James E. Hall, Jean Marie McDill, Beverly H. West
2nd edition
131860615, 978-0131860612
