Posted in Macroeconomics

Applied Computational Economics and Finance by Mario J. Miranda

By Mario J. Miranda

Excellent ebook for utilized economics with many examples and usefull Matlab codes. first-class and worthy Matlab toolkit.
However, the theoretical part is comparatively vulnerable and never coated good.

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Sample text

Function iteration, however, often converges even when the sufficiency conditions are not met. Given that the method is relatively easy to implement, it is often worth trying before attempting to use more robust, but ultimately more complex, methods, such as the Newton and quasi-Newton methods, which are discussed in the following sections. 1. 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.

In practice, the elasticity is estimated using the condition number of the matrix A, which for invertible A is defined by κ ≡ ||A|| · ||A−1 || The condition number of A is the least upper bound of the elasticity. The bound is tight in that for some data vector b, the condition number equals the elasticity. The condition number is always greater than or equal to one. Numerical analysts often use the rough rule of thumb that for each power of 10 in the condition number, one significant digit is lost in the computed solution vector x.

C. x = A−1 b, computing A−1 only once using the MATLAB function inv. 3. Prove theoretically that Gauss-Jacobi iteration applied to the linear equation Ax = b must converge if A is diagonally dominant. You will need to use the Contraction Mapping Theorem (Appendix A, p. 461) and the result that ||M y|| ≤ ||M|| ||y|| for any square matrix M and conformable vector y. 4. It is well known that a quadratic equation ax 2 + bx + c = 0 has two roots given by √ −b ± b2 − 4ac 2a There are, however, other mathematically correct ways of expressing the quadratic equation.

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