By Mario J. Miranda
Excellent ebook for utilized economics with many examples and usefull Matlab codes. first-class and invaluable Matlab toolkit.
However, the theoretical aspect is comparatively susceptible and never coated good.
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Additional resources for Applied Computational Economics and Finance
The technique is also applicable to a rootfinding problem f (x) = 0 by recasting it as the equivalent fixed-point problem x = x − f (x). Function iteration begins with the analyst supplying a guess x (0) for the fixed point of g. Subsequent iterates are generated using the simple iteration rule x (k+1) ← g x (k) Since g is continuous, if the iterates converge, they converge to a fixed point of g. In theory, function iteration is guaranteed to converge to a fixed point of g if g is differentiable and if the initial value of x supplied by the analyst is “sufficiently” close to a fixed point x ∗ of g at which g (x ∗ ) < 1.
The bisection method’s greatest strength is its robustness. In contrast to other rootfinding methods, the bisection method is guaranteed to compute a root to a prescribed tolerance Nonlinear Equations and Complementarity Problems 31 in a known number of iterations, provided valid data are entered. Specifically, the method computes a root to a precision in no more than log((b − a)/ )/ log(2) iterations. The bisection method, however, is applicable only to one-dimensional rootfinding problems and typically requires more iterations than other rootfinding methods to compute a root to a given precision, largely because it ignores information about the function’s curvature.
In this example, g possesses a unique fixed point x ∗ , which is graphically characterized by the intersection of g and the 45-degree line. The algorithm begins with the analyst supplying a guess x (0) for the fixed point of g. The next iterate x (1) is obtained by projecting upward to the g function and then rightward to the 45-degree line. Subsequent iterates are obtained by repeating the projection sequence, tracing out a step function. The process continues until the iterates converge. The CompEcon Toolbox includes a routine fixpoint that computes a fixed point of a multivariate function using function iteration.