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from Part I - Numerical Linear Algebra
Published online by Cambridge University Press: 29 September 2022
We present several methods for approximating the spectrum of a matrix. We start by providing coarse estimates using so-called Gershgoring disks. The stability, via the Bauer-Fike theorem is then analyzed. For Hermitian matrices we then present and analyze the power iteration method and its variants. The reduction to Hessenberg form, and the QR algorithm are then presented and analyzed. The chapter then concludes with a discussion of the Golub-Kahan algorithm to compute the SVD.
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