In Chapter 2 we have seen that in order to compute a singular-value decomposition of a matrix A, we need to have the eigenvalues of A T A. This process was illustrated in Example 2.6.3, where because of the small size of the problem, we were able to find the necessary eigenvalues by hand calculation. For larger problems, however, this is no longer possible, and we need to use a computer to find eigenvalues. Such problems arise, for example, in the study of oscillations, where the eigenfrequences are to be determined by discretizing the associated differential equation. In this chapter we discuss various methods for computing eigenvalues of matrices.
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