By Mario J. Miranda
First-class e-book for utilized economics with many examples and usefull Matlab codes. first-class and valuable Matlab toolkit.
However, the theoretical part is comparatively susceptible and never lined good.
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Example text
In the nonlinear rootfinding problem, a function f from Rn to Rn is given, and one must compute an n-vector x, called a root of f , that satisfies f (x) = 0 In the nonlinear fixed-point problem, a function g from Rn to Rn is given, and one must compute an n-vector x, called a fixed-point of g, that satisfies x = g(x) The two forms are equivalent. The rootfinding problem may be recast as a fixed-point problem by letting g(x) = x − f (x); conversely, the fixed-point problem may be recast as a rootfinding problem by letting f (x) = x − g(x).
B. Gauss-Jacobi iteration. c. Gauss-Seidel iteration. How many Gauss-Jacobi and Gauss-Seidel iterations are required to get answers that agree with the L-U decomposition solution to four significant digits? 2. Use the MATLAB function randn to generate a random 100-by-100 matrix A and a random 100-vector b. Then use the MATLAB functions tic and toc to compute the time needed to solve the linear equation Ax = b 1, 10, and 50 times for each of the following algorithms: a. x = A\b. b. x = U \(L\b), computing the L-U factors of A only once using the MATLAB function lu.
Therefore, it is possible to perform the operation (x*y)/y and have the result not equal x; instead it may be off by 1 in its least significant digit. Furthermore, if e1 + e2 (plus any adjustment arising from the division) is greater than 2d or less than −2d , the result cannot be represented. This is a situation known as overflow. In MATLAB, overflow produces a result that is set to inf or -inf. Further operations may produce sensible results, but, more often than not, the end result of overflow is useless.
