Linear Progr

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Chapter 9.

Root Finding and Nonlinear Sets of Equations

} a=b; fa=fb; if (fabs(d) > tol1) b += d; else b += SIGN(tol1,xm); fb=(*func)(b);

Move last best guess to a. Evaluate new trial root.

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} nrerror("Maximum number of iterations exceeded in zbrent"); return 0.0; Never get here. }

CITED REFERENCES AND FURTHER READING: Brent, R.P. 1973, Algorithms for Minimization without Derivatives (Englewood Cliffs, NJ: PrenticeHall), Chapters 3, 4. [1] Forsythe, G.E., Malcolm, M.A., and Moler, C.B. 1977, Computer Methods for Mathematical Computations (Englewood Cliffs, NJ: Prentice-Hall), §7.2.

9.4 Newton-Raphson Method Using Derivative
Perhaps the most celebrated of all one-dimensional root-finding routines is Newton’s method, also called the Newton-Raphson method. This method is distinguished from the methods of previous sections by the fact that it requires the evaluation of both the function f (x), and the derivative f (x), at arbitrary points x. The Newton-Raphson formula consists geometrically of extending the tangent line at a current point x i until it crosses zero, then setting the next guess x i+1 to the abscissa of that zero-crossing (see Figure 9.4.1). Algebraically, the method derives from the familiar Taylor series…...

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