By Mario J. Miranda
Excellent publication for utilized economics with many examples and usefull Matlab codes. first-class and worthwhile Matlab toolkit.
However, the theoretical part is comparatively vulnerable and never lined good.
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Extra resources for Applied Computational Economics and Finance
Consider the matrix 2 0 −1 2 4 2 −1 4 A= 2 −2 −2 3 −2 2 7 −3 The first stage of Gaussian elimination is designed to nullify the subdiagonal entries of the first column of the U matrix. The U matrix is updated by subtracting 2 times the first row from the second, subtracting 1 times the first row from the third, and subtracting −1 times the first row from the fourth. The L matrix, which initially equals the identity, is updated by storing the multipliers 2, 1, and −1 as the subdiagonal entries of its first column.
2e+040 Linear Equations and Computer Basics 15 In this example the computed answers are accurate to seven decimals up to n = 10. The accuracy, however, deteriorates rapidly after that point. In this example the matrix A is a member of a class of notoriously ill-conditioned matrices called the Vandermonde matrices, which we will encounter again in Chapter 6. Ill conditioning ultimately can be ascribed to the limited precision of computer arithmetic. The effects of ill conditioning can often be mitigated by performing computer arithmetic using the highest precision available on the computer.
If A is not invertible, Gaussian elimination will detect this fact by encountering a zero diagonal element in the U matrix that cannot be replaced with a nonzero element below it. 3 Rounding Error In practice, Gaussian elimination performed on a computer can sometimes render inaccurate solutions as a result of rounding errors. The effects of rounding errors, however, can often be controlled by pivoting. Consider the linear equation −M −1 1 1 1 x1 x2 = 1 2 where M is a large positive number. To solve this equation using Gaussian elimination, a single row operation is required: subtracting −M times the first row from the second row.